Challenges in Open-air Microwave Quantum Communication and Sensing

Mikel Sanz,1 Kirill G. Fedorov,2, 3 Frank Deppe,2, 3, 4 and Enrique Solano1, 5, 6

1Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080 Bilbao, Spain∗

2Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany3Physik-Department, Technische Universitat Munchen, D-85748 Garching, Germany4Nanosystems Initiative Munich (NIM), Schellingstrae 4, 80799 Munchen, Germany

5IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, E-48013 Bilbao, Spain6Department of Physics, Shanghai University, 200444 Shanghai, China

Quantum communication is a holy grail to achieve secure communication among a set of partners,since it is provably unbreakable by physical laws. Quantum sensing employs quantum entanglementas an extra resource to determine parameters by either using less resources or attaining a precisionunachievable in classical protocols. A paradigmatic example is the quantum radar, which allowsone to detect an object without being detected oneself, by making use of the additional assetprovided by quantum entanglement to reduce the intensity of the signal. In the optical regime,impressive technological advances have been reached in the last years, such as the first quantumcommunication between ground and satellites, as well as the first proof-of-principle experiments inquantum sensing. The development of microwave quantum technologies turned out, nonetheless,to be more challenging. Here, we will discuss the challenges regarding the use of microwaves forquantum communication and sensing. Based on this analysis, we propose a roadmap to achievereal-life applications in these fields.

I. INTRODUCTION

Quantum communication is a branch of quantum in-formation which makes use of quantum entanglement asa resource to protect and transmit through a quantumchannel information with higher capacity than any classi-cal channel and, when combined with quantum cryptog-raphy, with provable protection against eavesdropping.In recent years, the experimental progress in this areawith optical photons has been astonishing, including a143 km quantum communication between the Spanishislands of Tenerife and La Palma [1], a 96 km connectionbetween Sicily and Malta through a submarine cable [2],or the recent quantum communication and quantum keydistribution using satellites [3–6], among others.

Quantum sensing is defined as the use of quantum sys-tems and properties, especially entanglement, as an extraresource to perform a measurement of a physical quan-tity with higher accuracy or smaller number of classicalresources than any classical protocol [7]. Originally, theuse of light for quantum sensing was mainly focused onemploying continuous-variable quantum states squeezedbelow the vacuum. In this context, a particularly inter-esting example is the use of squeezed light for the de-tection of gravitational waves in LIGO [8]. A modifiedversion of the Hanbury-Brown-Twiss experiment usingentangled light allowed for the outperformance the spa-tial resolution of microscopes below the diffraction limit[9]. A particularly interesting application for our discus-sion is the application of entangled light to quantum illu-mination, in which instead of the resolution, the entan-glement is used to improve the contrast [10–12]. Finally,

∗ mikel.sanz@ehu.eus

it is noteworthy to mention that also impressive advanceshave been achieved in Heisenberg-limited interferometersby using Fock states [13].

II. STATE OF THE ART IN QUANTUMMICROWAVE TECHNOLOGY

The advances in the use of microwaves in the quantumregime for technological applications were more gradualthan with optical photons. The reasons are not onlyhistorical, but they also lie in technological difficultieswhich make the control of microwave photons much sub-tler than optical photons. In this section, we will firstaddress some of the most relevant physical and technolog-ical problems of propagating quantum microwaves. Af-terwards, we will briefly review the state of the art inexperiments and some relevant experimental proposals.

A. Technological Challenges for QuantumMicrowaves

• The most important challenge when employing mi-crowaves for quantum technologies when comparedwith optical photons is the requirement of cryogen-ics. Indeed, the thermal isolation required for pho-tons in the gigahertz regime is much higher than inthe terahertz regime. This can be shown by con-sidering the Bose-Einstein distribution, which esti-mates the number of photons per volume unit withfrequency between ν and ν + dν

n(ν) ∝ 1

ehνkbT − 1

, (1)

arX

iv:1

809.

0297

9v2

[qu

ant-

ph]

26

Dec

201

8

2

where T is the temperature. If we consider an opti-cal frequency of ν = 500 THz at room temperatureT = 300 K, then n(500 THz) ≈ 2× 10−35 photons.However, if we do the same for ν = 5 GHz, we ob-tain n(5 GHz) ≈ 1250 photons. Therefore, as theenergy is much smaller, many thermal microwavephotons are created, which is not favorable forquantum applications. This is the fundamental rea-son why superconducting circuits, which typicallyoperates in the 2− 7 GHz regime use cryogenics at30 mK, temperature at which n(5 GHz) ≈ 3×10−4

photons.

• The aforementioned fundamental difficulty due tothermal photons seems to limit possible applica-tions of quantum microwaves to intra-fridge en-vironments. This is sufficient for quantum com-puting applications with superconducting circuits,but only allows for proof-of-principle experimentsin quantum communication and sensing.

• Photodetectors are devices which transform pho-tons into an electric current, usually by means ofa p-n junction or the photoelectric effect. Theseeffects very well fit with optical frequencies, whatallows for the construction of photodetectors andphotocounters, for flying photons, i.e. for pho-tons which are not trapped inside a cavity. How-ever, this approach cannot be directly applied topropagating quantum microwaves and only pho-todetectors with limited efficiency (or photodetec-tors for trapped photons) have been constructedso far. Nonetheless, for most applications in quan-tum sensing and especially quantum illumination,efficient photodetection is mandatory [14, 15], thusfurther research in required in this area.

• The lack of efficient photodetectors reduces themeasurements achievable for propagating quantummicrowaves to the quantification of electromagneticfield quadratures.

B. Experimental State of the Art

Intra-fridge technology related to quantum microwaveshas experienced a strong advance in the last decadesdriven by the development of superconducting circuitsand superconducting qubits for quantum simulations andquantum computing. Profound improvements have beenperformed in the fabrication of purer superconductingthin field materials, in the accuracy of lithography, andin the efficiency of cooling down superconducting circuitswith the help of closed-cycle dilution refrigerators.

Important theoretical development and experimentalachievements towards quantum teleportation with dis-crete degrees of freedom [16] and continuous variables[17–19] in the microwave regime have appeared in the last

1

? 1

B

B

B

B

FIG. 1. A quantum radar makes use of quantum entangle-ment to enhance the accuracy of a radar or to reduce the useof photons to detect the presence of a low-reflectivity objectwith reflectivity, η 1, in a noisy thermal environment ρB .In the lab, two entangled beams |ΨSI〉 are prepared, send-ing one to the position in which the object might be, whilekeeping the other in the lab. Afterwards, a joint measure-ment of the reflected signal together with the beam in the labis performed. In comparison to classical light, the existenceof quantum correlations allows us to achieve up to 6 dB ofquantum advantage in terms of signal-to-noise ratio.

years. However, these experiments are currently still lim-ited to the intra-fridge environments or work in progress.

In the case of quantum illumination or quantummetrology employing quantum microwaves, there are noexperimental results to the best of our knowledge. Inquantum illumination, entangled radiation could be em-ployed to enhance the detection accuracy of a radar orto reduce the amount of photons demanded to detectthe presence of a low-reflectivity object in a noisy envi-ronment (detect it without being detected). In general,the idea consists in preparing a pair of entangled opticalor microwave beams and irradiating the target with oneof them, while preserving the other one in the lab. Incomparison to classical light, the existence of quantumcorrelations between the two beams allows us to declarethe presence or absence of the object with either a higheraccuracy or less resources, theoretically achieving up to6 dB of quantum advantage in terms of signal-to-noiseratio. From the theoretical point of view, the first appli-cation of quantum microwaves to quantum illuminationwas recently introduced in Ref. [21]. However, this ar-ticle avoids the problem of the microwave photodetectorby using a microwave-to-optics transducer and employingoptical photodetectors. Unfortunately, such a transducerhas turned out to be as technologically demanding asphotodetection in microwaves, and the efficiency of cur-rent implementations is not at all sufficient for practicalapplications. Other theory proposals in the microwaveregime aim at the detection of cloaked objects [15] or usequantum estimation techniques to obtain the optimal ob-servables to measure [14].

The lack of single-photon photodetectors for propa-gating microwaves is one of the main challenges for anypossible application of quantum microwaves in quantumcommunication and sensing. Physically, the reason ofthe difficulty in developing efficient microwave photode-

3

H2O<latexit sha1_base64="W43SapHTBFTCFlpJtp6XE3qa9dM=">AAAB9XicbZDLSsNAFIYnXmu9xbp0EyyCq5IUQZcFN91ZwV6gDWEyPWmHTi7MnGhLyKPoStSdL+IL+DZO2yy09V99c/5/4JzfTwRXaNvfxsbm1vbObmmvvH9weHRsnlQ6Kk4lgzaLRSx7PlUgeARt5Cigl0igoS+g609u5373EaTicfSAswTckI4iHnBGUY88szJAmGLWzL36ku5yz6zaNXshax2cAqqkUMszvwbDmKUhRMgEVarv2Am6GZXImYC8PEgVJJRN6Aj6GiMagnKzxe65dRHE0sIxWIv372xGQ6Vmoa8zIcWxWvXmw/+8forBjZvxKEkRIqYj2gtSYWFszSuwhlwCQzHTQJnkekuLjamkDHVRZX2+s3rsOnTqNceuOfdX1YZTFFEiZ+ScXBKHXJMGaZIWaRNGpuSFvJMP48l4Nl6Nt2V0wyj+nJI/Mj5/AEVmkj0=</latexit><latexit sha1_base64="W43SapHTBFTCFlpJtp6XE3qa9dM=">AAAB9XicbZDLSsNAFIYnXmu9xbp0EyyCq5IUQZcFN91ZwV6gDWEyPWmHTi7MnGhLyKPoStSdL+IL+DZO2yy09V99c/5/4JzfTwRXaNvfxsbm1vbObmmvvH9weHRsnlQ6Kk4lgzaLRSx7PlUgeARt5Cigl0igoS+g609u5373EaTicfSAswTckI4iHnBGUY88szJAmGLWzL36ku5yz6zaNXshax2cAqqkUMszvwbDmKUhRMgEVarv2Am6GZXImYC8PEgVJJRN6Aj6GiMagnKzxe65dRHE0sIxWIv372xGQ6Vmoa8zIcWxWvXmw/+8forBjZvxKEkRIqYj2gtSYWFszSuwhlwCQzHTQJnkekuLjamkDHVRZX2+s3rsOnTqNceuOfdX1YZTFFEiZ+ScXBKHXJMGaZIWaRNGpuSFvJMP48l4Nl6Nt2V0wyj+nJI/Mj5/AEVmkj0=</latexit><latexit sha1_base64="W43SapHTBFTCFlpJtp6XE3qa9dM=">AAAB9XicbZDLSsNAFIYnXmu9xbp0EyyCq5IUQZcFN91ZwV6gDWEyPWmHTi7MnGhLyKPoStSdL+IL+DZO2yy09V99c/5/4JzfTwRXaNvfxsbm1vbObmmvvH9weHRsnlQ6Kk4lgzaLRSx7PlUgeARt5Cigl0igoS+g609u5373EaTicfSAswTckI4iHnBGUY88szJAmGLWzL36ku5yz6zaNXshax2cAqqkUMszvwbDmKUhRMgEVarv2Am6GZXImYC8PEgVJJRN6Aj6GiMagnKzxe65dRHE0sIxWIv372xGQ6Vmoa8zIcWxWvXmw/+8forBjZvxKEkRIqYj2gtSYWFszSuwhlwCQzHTQJnkekuLjamkDHVRZX2+s3rsOnTqNceuOfdX1YZTFFEiZ+ScXBKHXJMGaZIWaRNGpuSFvJMP48l4Nl6Nt2V0wyj+nJI/Mj5/AEVmkj0=</latexit><latexit sha1_base64="W43SapHTBFTCFlpJtp6XE3qa9dM=">AAAB9XicbZDLSsNAFIYnXmu9xbp0EyyCq5IUQZcFN91ZwV6gDWEyPWmHTi7MnGhLyKPoStSdL+IL+DZO2yy09V99c/5/4JzfTwRXaNvfxsbm1vbObmmvvH9weHRsnlQ6Kk4lgzaLRSx7PlUgeARt5Cigl0igoS+g609u5373EaTicfSAswTckI4iHnBGUY88szJAmGLWzL36ku5yz6zaNXshax2cAqqkUMszvwbDmKUhRMgEVarv2Am6GZXImYC8PEgVJJRN6Aj6GiMagnKzxe65dRHE0sIxWIv372xGQ6Vmoa8zIcWxWvXmw/+8forBjZvxKEkRIqYj2gtSYWFszSuwhlwCQzHTQJnkekuLjamkDHVRZX2+s3rsOnTqNceuOfdX1YZTFFEiZ+ScXBKHXJMGaZIWaRNGpuSFvJMP48l4Nl6Nt2V0wyj+nJI/Mj5/AEVmkj0=</latexit>

H2O<latexit sha1_base64="W43SapHTBFTCFlpJtp6XE3qa9dM=">AAAB9XicbZDLSsNAFIYnXmu9xbp0EyyCq5IUQZcFN91ZwV6gDWEyPWmHTi7MnGhLyKPoStSdL+IL+DZO2yy09V99c/5/4JzfTwRXaNvfxsbm1vbObmmvvH9weHRsnlQ6Kk4lgzaLRSx7PlUgeARt5Cigl0igoS+g609u5373EaTicfSAswTckI4iHnBGUY88szJAmGLWzL36ku5yz6zaNXshax2cAqqkUMszvwbDmKUhRMgEVarv2Am6GZXImYC8PEgVJJRN6Aj6GiMagnKzxe65dRHE0sIxWIv372xGQ6Vmoa8zIcWxWvXmw/+8forBjZvxKEkRIqYj2gtSYWFszSuwhlwCQzHTQJnkekuLjamkDHVRZX2+s3rsOnTqNceuOfdX1YZTFFEiZ+ScXBKHXJMGaZIWaRNGpuSFvJMP48l4Nl6Nt2V0wyj+nJI/Mj5/AEVmkj0=</latexit><latexit sha1_base64="W43SapHTBFTCFlpJtp6XE3qa9dM=">AAAB9XicbZDLSsNAFIYnXmu9xbp0EyyCq5IUQZcFN91ZwV6gDWEyPWmHTi7MnGhLyKPoStSdL+IL+DZO2yy09V99c/5/4JzfTwRXaNvfxsbm1vbObmmvvH9weHRsnlQ6Kk4lgzaLRSx7PlUgeARt5Cigl0igoS+g609u5373EaTicfSAswTckI4iHnBGUY88szJAmGLWzL36ku5yz6zaNXshax2cAqqkUMszvwbDmKUhRMgEVarv2Am6GZXImYC8PEgVJJRN6Aj6GiMagnKzxe65dRHE0sIxWIv372xGQ6Vmoa8zIcWxWvXmw/+8forBjZvxKEkRIqYj2gtSYWFszSuwhlwCQzHTQJnkekuLjamkDHVRZX2+s3rsOnTqNceuOfdX1YZTFFEiZ+ScXBKHXJMGaZIWaRNGpuSFvJMP48l4Nl6Nt2V0wyj+nJI/Mj5/AEVmkj0=</latexit><latexit sha1_base64="W43SapHTBFTCFlpJtp6XE3qa9dM=">AAAB9XicbZDLSsNAFIYnXmu9xbp0EyyCq5IUQZcFN91ZwV6gDWEyPWmHTi7MnGhLyKPoStSdL+IL+DZO2yy09V99c/5/4JzfTwRXaNvfxsbm1vbObmmvvH9weHRsnlQ6Kk4lgzaLRSx7PlUgeARt5Cigl0igoS+g609u5373EaTicfSAswTckI4iHnBGUY88szJAmGLWzL36ku5yz6zaNXshax2cAqqkUMszvwbDmKUhRMgEVarv2Am6GZXImYC8PEgVJJRN6Aj6GiMagnKzxe65dRHE0sIxWIv372xGQ6Vmoa8zIcWxWvXmw/+8forBjZvxKEkRIqYj2gtSYWFszSuwhlwCQzHTQJnkekuLjamkDHVRZX2+s3rsOnTqNceuOfdX1YZTFFEiZ+ScXBKHXJMGaZIWaRNGpuSFvJMP48l4Nl6Nt2V0wyj+nJI/Mj5/AEVmkj0=</latexit><latexit sha1_base64="W43SapHTBFTCFlpJtp6XE3qa9dM=">AAAB9XicbZDLSsNAFIYnXmu9xbp0EyyCq5IUQZcFN91ZwV6gDWEyPWmHTi7MnGhLyKPoStSdL+IL+DZO2yy09V99c/5/4JzfTwRXaNvfxsbm1vbObmmvvH9weHRsnlQ6Kk4lgzaLRSx7PlUgeARt5Cigl0igoS+g609u5373EaTicfSAswTckI4iHnBGUY88szJAmGLWzL36ku5yz6zaNXshax2cAqqkUMszvwbDmKUhRMgEVarv2Am6GZXImYC8PEgVJJRN6Aj6GiMagnKzxe65dRHE0sIxWIv372xGQ6Vmoa8zIcWxWvXmw/+8forBjZvxKEkRIqYj2gtSYWFszSuwhlwCQzHTQJnkekuLjamkDHVRZX2+s3rsOnTqNceuOfdX1YZTFFEiZ+ScXBKHXJMGaZIWaRNGpuSFvJMP48l4Nl6Nt2V0wyj+nJI/Mj5/AEVmkj0=</latexit>

O2<latexit sha1_base64="Ip0Z5hYj+DTLQfHWnU3Dtg24DkA=">AAAB9nicbZDLSsNAFIYn9VbrLdqlm8FScFWSIuiy4MadFewF2lAm09N26OTCzIk0hL6KrkTd+SC+gG/jtAbR1n/1zfn/gXN+P5ZCo+N8WoWNza3tneJuaW//4PDIPj5p6yhRHFo8kpHq+kyDFCG0UKCEbqyABb6Ejj+9XvidB1BaROE9pjF4ARuHYiQ4QzMa2OU+wgyz2/mgXv1Bu+LUnKXoOrg5VEiu5sD+6A8jngQQIpdM657rxOhlTKHgEualfqIhZnzKxtAzGLIAtJctl5/T6ihSFCdAl+/f2YwFWqeBbzIBw4le9RbD/7xegqMrLxNhnCCE3ESMN0okxYguOqBDoYCjTA0wroTZkvIJU4yjaapkzndXj12Hdr3mOjX37qLScPMiiuSUnJFz4pJL0iA3pElahJOUPJFX8mbNrEfr2Xr5jhas/E+Z/JH1/gWxm5Jz</latexit><latexit sha1_base64="Ip0Z5hYj+DTLQfHWnU3Dtg24DkA=">AAAB9nicbZDLSsNAFIYn9VbrLdqlm8FScFWSIuiy4MadFewF2lAm09N26OTCzIk0hL6KrkTd+SC+gG/jtAbR1n/1zfn/gXN+P5ZCo+N8WoWNza3tneJuaW//4PDIPj5p6yhRHFo8kpHq+kyDFCG0UKCEbqyABb6Ejj+9XvidB1BaROE9pjF4ARuHYiQ4QzMa2OU+wgyz2/mgXv1Bu+LUnKXoOrg5VEiu5sD+6A8jngQQIpdM657rxOhlTKHgEualfqIhZnzKxtAzGLIAtJctl5/T6ihSFCdAl+/f2YwFWqeBbzIBw4le9RbD/7xegqMrLxNhnCCE3ESMN0okxYguOqBDoYCjTA0wroTZkvIJU4yjaapkzndXj12Hdr3mOjX37qLScPMiiuSUnJFz4pJL0iA3pElahJOUPJFX8mbNrEfr2Xr5jhas/E+Z/JH1/gWxm5Jz</latexit><latexit sha1_base64="Ip0Z5hYj+DTLQfHWnU3Dtg24DkA=">AAAB9nicbZDLSsNAFIYn9VbrLdqlm8FScFWSIuiy4MadFewF2lAm09N26OTCzIk0hL6KrkTd+SC+gG/jtAbR1n/1zfn/gXN+P5ZCo+N8WoWNza3tneJuaW//4PDIPj5p6yhRHFo8kpHq+kyDFCG0UKCEbqyABb6Ejj+9XvidB1BaROE9pjF4ARuHYiQ4QzMa2OU+wgyz2/mgXv1Bu+LUnKXoOrg5VEiu5sD+6A8jngQQIpdM657rxOhlTKHgEualfqIhZnzKxtAzGLIAtJctl5/T6ihSFCdAl+/f2YwFWqeBbzIBw4le9RbD/7xegqMrLxNhnCCE3ESMN0okxYguOqBDoYCjTA0wroTZkvIJU4yjaapkzndXj12Hdr3mOjX37qLScPMiiuSUnJFz4pJL0iA3pElahJOUPJFX8mbNrEfr2Xr5jhas/E+Z/JH1/gWxm5Jz</latexit><latexit sha1_base64="Ip0Z5hYj+DTLQfHWnU3Dtg24DkA=">AAAB9nicbZDLSsNAFIYn9VbrLdqlm8FScFWSIuiy4MadFewF2lAm09N26OTCzIk0hL6KrkTd+SC+gG/jtAbR1n/1zfn/gXN+P5ZCo+N8WoWNza3tneJuaW//4PDIPj5p6yhRHFo8kpHq+kyDFCG0UKCEbqyABb6Ejj+9XvidB1BaROE9pjF4ARuHYiQ4QzMa2OU+wgyz2/mgXv1Bu+LUnKXoOrg5VEiu5sD+6A8jngQQIpdM657rxOhlTKHgEualfqIhZnzKxtAzGLIAtJctl5/T6ihSFCdAl+/f2YwFWqeBbzIBw4le9RbD/7xegqMrLxNhnCCE3ESMN0okxYguOqBDoYCjTA0wroTZkvIJU4yjaapkzndXj12Hdr3mOjX37qLScPMiiuSUnJFz4pJL0iA3pElahJOUPJFX8mbNrEfr2Xr5jhas/E+Z/JH1/gWxm5Jz</latexit>

CO2<latexit sha1_base64="rcxK4SyOtxJQ2trDfXFmDssao14=">AAAB9XicbVC7TsNAEDzzDOFlQkljESFRRXaEBGWkNHQEiTykxLLOl3VyyvmhuzUksvwpUCGg40f4Af6GS+ICEqbZ2Z1ZaXf8RHCFtv1tbGxube/slvbK+weHR8fmSaWj4lQyaLNYxLLnUwWCR9BGjgJ6iQQa+gK6/qQ517uPIBWPowecJeCGdBTxgDOKeuSZlQHCFLNmvqx3uVf3zKpdsxew1olTkCop0PLMr8EwZmkIETJBleo7doJuRiVyJiAvD1IFCWUTOoK+phENQbnZ4vbcughiaeEYrEX/25vRUKlZ6GtPSHGsVrX58D+tn2Jw42Y8SlKEiGmL1oJUWBhb8wisIZfAUMw0oUxyfaXFxlRShjqosn7fWX12nXTqNceuOfdX1YZTBFEiZ+ScXBKHXJMGuSUt0iaMTMkLeScfxpPxbLwab0vrhlHsnJI/MD5/AEABkjg=</latexit><latexit sha1_base64="rcxK4SyOtxJQ2trDfXFmDssao14=">AAAB9XicbVC7TsNAEDzzDOFlQkljESFRRXaEBGWkNHQEiTykxLLOl3VyyvmhuzUksvwpUCGg40f4Af6GS+ICEqbZ2Z1ZaXf8RHCFtv1tbGxube/slvbK+weHR8fmSaWj4lQyaLNYxLLnUwWCR9BGjgJ6iQQa+gK6/qQ517uPIBWPowecJeCGdBTxgDOKeuSZlQHCFLNmvqx3uVf3zKpdsxew1olTkCop0PLMr8EwZmkIETJBleo7doJuRiVyJiAvD1IFCWUTOoK+phENQbnZ4vbcughiaeEYrEX/25vRUKlZ6GtPSHGsVrX58D+tn2Jw42Y8SlKEiGmL1oJUWBhb8wisIZfAUMw0oUxyfaXFxlRShjqosn7fWX12nXTqNceuOfdX1YZTBFEiZ+ScXBKHXJMGuSUt0iaMTMkLeScfxpPxbLwab0vrhlHsnJI/MD5/AEABkjg=</latexit><latexit sha1_base64="rcxK4SyOtxJQ2trDfXFmDssao14=">AAAB9XicbVC7TsNAEDzzDOFlQkljESFRRXaEBGWkNHQEiTykxLLOl3VyyvmhuzUksvwpUCGg40f4Af6GS+ICEqbZ2Z1ZaXf8RHCFtv1tbGxube/slvbK+weHR8fmSaWj4lQyaLNYxLLnUwWCR9BGjgJ6iQQa+gK6/qQ517uPIBWPowecJeCGdBTxgDOKeuSZlQHCFLNmvqx3uVf3zKpdsxew1olTkCop0PLMr8EwZmkIETJBleo7doJuRiVyJiAvD1IFCWUTOoK+phENQbnZ4vbcughiaeEYrEX/25vRUKlZ6GtPSHGsVrX58D+tn2Jw42Y8SlKEiGmL1oJUWBhb8wisIZfAUMw0oUxyfaXFxlRShjqosn7fWX12nXTqNceuOfdX1YZTBFEiZ+ScXBKHXJMGuSUt0iaMTMkLeScfxpPxbLwab0vrhlHsnJI/MD5/AEABkjg=</latexit><latexit sha1_base64="rcxK4SyOtxJQ2trDfXFmDssao14=">AAAB9XicbVC7TsNAEDzzDOFlQkljESFRRXaEBGWkNHQEiTykxLLOl3VyyvmhuzUksvwpUCGg40f4Af6GS+ICEqbZ2Z1ZaXf8RHCFtv1tbGxube/slvbK+weHR8fmSaWj4lQyaLNYxLLnUwWCR9BGjgJ6iQQa+gK6/qQ517uPIBWPowecJeCGdBTxgDOKeuSZlQHCFLNmvqx3uVf3zKpdsxew1olTkCop0PLMr8EwZmkIETJBleo7doJuRiVyJiAvD1IFCWUTOoK+phENQbnZ4vbcughiaeEYrEX/25vRUKlZ6GtPSHGsVrX58D+tn2Jw42Y8SlKEiGmL1oJUWBhb8wisIZfAUMw0oUxyfaXFxlRShjqosn7fWX12nXTqNceuOfdX1YZTBFEiZ+ScXBKHXJMGuSUt0iaMTMkLeScfxpPxbLwab0vrhlHsnJI/MD5/AEABkjg=</latexit>

1GHz<latexit sha1_base64="LRazK05G2NLb8Bx7zTIyxz90h2c=">AAAB7HicbZDNTsJAFIWn+If4h7p0M5GYuCKtMdEliQtZYiJgUhoyHW5hwrTTzNwaseEtdGXUnU/jC/g2DtiFgmf1zT1nkntumEph0HW/nNLK6tr6RnmzsrW9s7tX3T/oGJVpDm2upNJ3ITMgRQJtFCjhLtXA4lBCNxxfzfzuPWgjVHKLkxSCmA0TEQnO0I58r4fwgPl183Har9bcujsXXQavgBop1OpXP3sDxbMYEuSSGeN7bopBzjQKLmFa6WUGUsbHbAi+xYTFYIJ8vvKUnkRKUxwBnb9/Z3MWGzOJQ5uJGY7Mojcb/uf5GUaXQS6SNENIuI1YL8okRUVnzelAaOAoJxYY18JuSfmIacbR3qdi63uLZZehc1b33Lp3c15reMUhyuSIHJNT4pEL0iBN0iJtwokiz+SNvDuJ8+S8OK8/0ZJT/Dkkf+R8fAMczI6/</latexit><latexit sha1_base64="LRazK05G2NLb8Bx7zTIyxz90h2c=">AAAB7HicbZDNTsJAFIWn+If4h7p0M5GYuCKtMdEliQtZYiJgUhoyHW5hwrTTzNwaseEtdGXUnU/jC/g2DtiFgmf1zT1nkntumEph0HW/nNLK6tr6RnmzsrW9s7tX3T/oGJVpDm2upNJ3ITMgRQJtFCjhLtXA4lBCNxxfzfzuPWgjVHKLkxSCmA0TEQnO0I58r4fwgPl183Har9bcujsXXQavgBop1OpXP3sDxbMYEuSSGeN7bopBzjQKLmFa6WUGUsbHbAi+xYTFYIJ8vvKUnkRKUxwBnb9/Z3MWGzOJQ5uJGY7Mojcb/uf5GUaXQS6SNENIuI1YL8okRUVnzelAaOAoJxYY18JuSfmIacbR3qdi63uLZZehc1b33Lp3c15reMUhyuSIHJNT4pEL0iBN0iJtwokiz+SNvDuJ8+S8OK8/0ZJT/Dkkf+R8fAMczI6/</latexit><latexit sha1_base64="LRazK05G2NLb8Bx7zTIyxz90h2c=">AAAB7HicbZDNTsJAFIWn+If4h7p0M5GYuCKtMdEliQtZYiJgUhoyHW5hwrTTzNwaseEtdGXUnU/jC/g2DtiFgmf1zT1nkntumEph0HW/nNLK6tr6RnmzsrW9s7tX3T/oGJVpDm2upNJ3ITMgRQJtFCjhLtXA4lBCNxxfzfzuPWgjVHKLkxSCmA0TEQnO0I58r4fwgPl183Har9bcujsXXQavgBop1OpXP3sDxbMYEuSSGeN7bopBzjQKLmFa6WUGUsbHbAi+xYTFYIJ8vvKUnkRKUxwBnb9/Z3MWGzOJQ5uJGY7Mojcb/uf5GUaXQS6SNENIuI1YL8okRUVnzelAaOAoJxYY18JuSfmIacbR3qdi63uLZZehc1b33Lp3c15reMUhyuSIHJNT4pEL0iBN0iJtwokiz+SNvDuJ8+S8OK8/0ZJT/Dkkf+R8fAMczI6/</latexit><latexit sha1_base64="LRazK05G2NLb8Bx7zTIyxz90h2c=">AAAB7HicbZDNTsJAFIWn+If4h7p0M5GYuCKtMdEliQtZYiJgUhoyHW5hwrTTzNwaseEtdGXUnU/jC/g2DtiFgmf1zT1nkntumEph0HW/nNLK6tr6RnmzsrW9s7tX3T/oGJVpDm2upNJ3ITMgRQJtFCjhLtXA4lBCNxxfzfzuPWgjVHKLkxSCmA0TEQnO0I58r4fwgPl183Har9bcujsXXQavgBop1OpXP3sDxbMYEuSSGeN7bopBzjQKLmFa6WUGUsbHbAi+xYTFYIJ8vvKUnkRKUxwBnb9/Z3MWGzOJQ5uJGY7Mojcb/uf5GUaXQS6SNENIuI1YL8okRUVnzelAaOAoJxYY18JuSfmIacbR3qdi63uLZZehc1b33Lp3c15reMUhyuSIHJNT4pEL0iBN0iJtwokiz+SNvDuJ8+S8OK8/0ZJT/Dkkf+R8fAMczI6/</latexit>

10GHz<latexit sha1_base64="CqMR5a7lLH2Q/9cCLpVN30Bhv+Y=">AAAB7XicbZDNTsJAFIWn+If4h7p000hMXJGOMdEliQtZYiJgQhsyHW5hwrTTzNwaseExdGXUnS/jC/g2DtiFgmf1zT1nkntumEph0PO+nNLK6tr6RnmzsrW9s7tX3T/oGJVpDm2upNJ3ITMgRQJtFCjhLtXA4lBCNxxfzfzuPWgjVHKLkxSCmA0TEQnO0I586vkID5hfNx+n/WrNq3tzuctAC6iRQq1+9dMfKJ7FkCCXzJge9VIMcqZRcAnTip8ZSBkfsyH0LCYsBhPk852n7kmktIsjcOfv39mcxcZM4tBmYoYjs+jNhv95vQyjyyAXSZohJNxGrBdl0kXlzqq7A6GBo5xYYFwLu6XLR0wzjvZAFVufLpZdhs5ZnXp1enNea9DiEGVyRI7JKaHkgjRIk7RIm3CSkmfyRt4d5Tw5L87rT7TkFH8OyR85H9+Lb475</latexit><latexit sha1_base64="CqMR5a7lLH2Q/9cCLpVN30Bhv+Y=">AAAB7XicbZDNTsJAFIWn+If4h7p000hMXJGOMdEliQtZYiJgQhsyHW5hwrTTzNwaseExdGXUnS/jC/g2DtiFgmf1zT1nkntumEph0PO+nNLK6tr6RnmzsrW9s7tX3T/oGJVpDm2upNJ3ITMgRQJtFCjhLtXA4lBCNxxfzfzuPWgjVHKLkxSCmA0TEQnO0I586vkID5hfNx+n/WrNq3tzuctAC6iRQq1+9dMfKJ7FkCCXzJge9VIMcqZRcAnTip8ZSBkfsyH0LCYsBhPk852n7kmktIsjcOfv39mcxcZM4tBmYoYjs+jNhv95vQyjyyAXSZohJNxGrBdl0kXlzqq7A6GBo5xYYFwLu6XLR0wzjvZAFVufLpZdhs5ZnXp1enNea9DiEGVyRI7JKaHkgjRIk7RIm3CSkmfyRt4d5Tw5L87rT7TkFH8OyR85H9+Lb475</latexit><latexit sha1_base64="CqMR5a7lLH2Q/9cCLpVN30Bhv+Y=">AAAB7XicbZDNTsJAFIWn+If4h7p000hMXJGOMdEliQtZYiJgQhsyHW5hwrTTzNwaseExdGXUnS/jC/g2DtiFgmf1zT1nkntumEph0PO+nNLK6tr6RnmzsrW9s7tX3T/oGJVpDm2upNJ3ITMgRQJtFCjhLtXA4lBCNxxfzfzuPWgjVHKLkxSCmA0TEQnO0I586vkID5hfNx+n/WrNq3tzuctAC6iRQq1+9dMfKJ7FkCCXzJge9VIMcqZRcAnTip8ZSBkfsyH0LCYsBhPk852n7kmktIsjcOfv39mcxcZM4tBmYoYjs+jNhv95vQyjyyAXSZohJNxGrBdl0kXlzqq7A6GBo5xYYFwLu6XLR0wzjvZAFVufLpZdhs5ZnXp1enNea9DiEGVyRI7JKaHkgjRIk7RIm3CSkmfyRt4d5Tw5L87rT7TkFH8OyR85H9+Lb475</latexit><latexit sha1_base64="CqMR5a7lLH2Q/9cCLpVN30Bhv+Y=">AAAB7XicbZDNTsJAFIWn+If4h7p000hMXJGOMdEliQtZYiJgQhsyHW5hwrTTzNwaseExdGXUnS/jC/g2DtiFgmf1zT1nkntumEph0PO+nNLK6tr6RnmzsrW9s7tX3T/oGJVpDm2upNJ3ITMgRQJtFCjhLtXA4lBCNxxfzfzuPWgjVHKLkxSCmA0TEQnO0I586vkID5hfNx+n/WrNq3tzuctAC6iRQq1+9dMfKJ7FkCCXzJge9VIMcqZRcAnTip8ZSBkfsyH0LCYsBhPk852n7kmktIsjcOfv39mcxcZM4tBmYoYjs+jNhv95vQyjyyAXSZohJNxGrBdl0kXlzqq7A6GBo5xYYFwLu6XLR0wzjvZAFVufLpZdhs5ZnXp1enNea9DiEGVyRI7JKaHkgjRIk7RIm3CSkmfyRt4d5Tw5L87rT7TkFH8OyR85H9+Lb475</latexit>

100GHz<latexit sha1_base64="ej9+eDP7iFeTM1oJ5R5YNB+UOe8=">AAAB7nicbZDLTgIxFIY7eEO8oS7dTCQmrkhrTHRJ4kKWmMglgQnplDPQ0LnYnjHihNfQlVF3Powv4NtYcBYK/quv5/+bnP/4iZIGKf1yCiura+sbxc3S1vbO7l55/6Bl4lQLaIpYxbrjcwNKRtBEiQo6iQYe+gra/vhq5rfvQRsZR7c4ScAL+TCSgRQc7chjlPYQHjC7rj9O++UKrdK53GVgOVRIrka//NkbxCINIUKhuDFdRhP0Mq5RCgXTUi81kHAx5kPoWox4CMbL5ktP3ZMg1i6OwJ2/f2czHhozCX2bCTmOzKI3G/7ndVMMLr1MRkmKEAkbsV6QKhdjd9bdHUgNAtXEAhda2i1dMeKaC7QXKtn6bLHsMrTOqoxW2c15pcbyQxTJETkmp4SRC1IjddIgTSLIHXkmb+TdSZwn58V5/YkWnPzPIfkj5+Mb+kSPMw==</latexit><latexit sha1_base64="ej9+eDP7iFeTM1oJ5R5YNB+UOe8=">AAAB7nicbZDLTgIxFIY7eEO8oS7dTCQmrkhrTHRJ4kKWmMglgQnplDPQ0LnYnjHihNfQlVF3Powv4NtYcBYK/quv5/+bnP/4iZIGKf1yCiura+sbxc3S1vbO7l55/6Bl4lQLaIpYxbrjcwNKRtBEiQo6iQYe+gra/vhq5rfvQRsZR7c4ScAL+TCSgRQc7chjlPYQHjC7rj9O++UKrdK53GVgOVRIrka//NkbxCINIUKhuDFdRhP0Mq5RCgXTUi81kHAx5kPoWox4CMbL5ktP3ZMg1i6OwJ2/f2czHhozCX2bCTmOzKI3G/7ndVMMLr1MRkmKEAkbsV6QKhdjd9bdHUgNAtXEAhda2i1dMeKaC7QXKtn6bLHsMrTOqoxW2c15pcbyQxTJETkmp4SRC1IjddIgTSLIHXkmb+TdSZwn58V5/YkWnPzPIfkj5+Mb+kSPMw==</latexit><latexit sha1_base64="ej9+eDP7iFeTM1oJ5R5YNB+UOe8=">AAAB7nicbZDLTgIxFIY7eEO8oS7dTCQmrkhrTHRJ4kKWmMglgQnplDPQ0LnYnjHihNfQlVF3Powv4NtYcBYK/quv5/+bnP/4iZIGKf1yCiura+sbxc3S1vbO7l55/6Bl4lQLaIpYxbrjcwNKRtBEiQo6iQYe+gra/vhq5rfvQRsZR7c4ScAL+TCSgRQc7chjlPYQHjC7rj9O++UKrdK53GVgOVRIrka//NkbxCINIUKhuDFdRhP0Mq5RCgXTUi81kHAx5kPoWox4CMbL5ktP3ZMg1i6OwJ2/f2czHhozCX2bCTmOzKI3G/7ndVMMLr1MRkmKEAkbsV6QKhdjd9bdHUgNAtXEAhda2i1dMeKaC7QXKtn6bLHsMrTOqoxW2c15pcbyQxTJETkmp4SRC1IjddIgTSLIHXkmb+TdSZwn58V5/YkWnPzPIfkj5+Mb+kSPMw==</latexit><latexit sha1_base64="ej9+eDP7iFeTM1oJ5R5YNB+UOe8=">AAAB7nicbZDLTgIxFIY7eEO8oS7dTCQmrkhrTHRJ4kKWmMglgQnplDPQ0LnYnjHihNfQlVF3Powv4NtYcBYK/quv5/+bnP/4iZIGKf1yCiura+sbxc3S1vbO7l55/6Bl4lQLaIpYxbrjcwNKRtBEiQo6iQYe+gra/vhq5rfvQRsZR7c4ScAL+TCSgRQc7chjlPYQHjC7rj9O++UKrdK53GVgOVRIrka//NkbxCINIUKhuDFdRhP0Mq5RCgXTUi81kHAx5kPoWox4CMbL5ktP3ZMg1i6OwJ2/f2czHhozCX2bCTmOzKI3G/7ndVMMLr1MRkmKEAkbsV6QKhdjd9bdHUgNAtXEAhda2i1dMeKaC7QXKtn6bLHsMrTOqoxW2c15pcbyQxTJETkmp4SRC1IjddIgTSLIHXkmb+TdSZwn58V5/YkWnPzPIfkj5+Mb+kSPMw==</latexit>

1THz<latexit sha1_base64="bZZnPVqvlbyyi1ZgYTqv2uNOt+E=">AAAB7HicbZDLSgMxFIYzXmu9VV26CRbBVZmIoMuCmy4r9AbToWTSM21o5kJyRqxD30JXou58Gl/AtzGts9DWf/Xl/H/g/CdIlTToul/O2vrG5tZ2aae8u7d/cFg5Ou6YJNMC2iJRie4F3ICSMbRRooJeqoFHgYJuMLmd+9170EYmcQunKfgRH8UylIKjHXmsj/CAeavxOBtUqm7NXYiuAiugSgo1B5XP/jARWQQxCsWN8Zibop9zjVIomJX7mYGUiwkfgWcx5hEYP1+sPKPnYaIpjoEu3r+zOY+MmUaBzUQcx2bZmw//87wMwxs/l3GaIcTCRqwXZopiQufN6VBqEKimFrjQ0m5JxZhrLtDep2zrs+Wyq9C5rDG3xu6uqnVWHKJETskZuSCMXJM6aZAmaRNBEvJM3si7EztPzovz+hNdc4o/J+SPnI9vMFmOzA==</latexit><latexit sha1_base64="bZZnPVqvlbyyi1ZgYTqv2uNOt+E=">AAAB7HicbZDLSgMxFIYzXmu9VV26CRbBVZmIoMuCmy4r9AbToWTSM21o5kJyRqxD30JXou58Gl/AtzGts9DWf/Xl/H/g/CdIlTToul/O2vrG5tZ2aae8u7d/cFg5Ou6YJNMC2iJRie4F3ICSMbRRooJeqoFHgYJuMLmd+9170EYmcQunKfgRH8UylIKjHXmsj/CAeavxOBtUqm7NXYiuAiugSgo1B5XP/jARWQQxCsWN8Zibop9zjVIomJX7mYGUiwkfgWcx5hEYP1+sPKPnYaIpjoEu3r+zOY+MmUaBzUQcx2bZmw//87wMwxs/l3GaIcTCRqwXZopiQufN6VBqEKimFrjQ0m5JxZhrLtDep2zrs+Wyq9C5rDG3xu6uqnVWHKJETskZuSCMXJM6aZAmaRNBEvJM3si7EztPzovz+hNdc4o/J+SPnI9vMFmOzA==</latexit><latexit sha1_base64="bZZnPVqvlbyyi1ZgYTqv2uNOt+E=">AAAB7HicbZDLSgMxFIYzXmu9VV26CRbBVZmIoMuCmy4r9AbToWTSM21o5kJyRqxD30JXou58Gl/AtzGts9DWf/Xl/H/g/CdIlTToul/O2vrG5tZ2aae8u7d/cFg5Ou6YJNMC2iJRie4F3ICSMbRRooJeqoFHgYJuMLmd+9170EYmcQunKfgRH8UylIKjHXmsj/CAeavxOBtUqm7NXYiuAiugSgo1B5XP/jARWQQxCsWN8Zibop9zjVIomJX7mYGUiwkfgWcx5hEYP1+sPKPnYaIpjoEu3r+zOY+MmUaBzUQcx2bZmw//87wMwxs/l3GaIcTCRqwXZopiQufN6VBqEKimFrjQ0m5JxZhrLtDep2zrs+Wyq9C5rDG3xu6uqnVWHKJETskZuSCMXJM6aZAmaRNBEvJM3si7EztPzovz+hNdc4o/J+SPnI9vMFmOzA==</latexit><latexit sha1_base64="bZZnPVqvlbyyi1ZgYTqv2uNOt+E=">AAAB7HicbZDLSgMxFIYzXmu9VV26CRbBVZmIoMuCmy4r9AbToWTSM21o5kJyRqxD30JXou58Gl/AtzGts9DWf/Xl/H/g/CdIlTToul/O2vrG5tZ2aae8u7d/cFg5Ou6YJNMC2iJRie4F3ICSMbRRooJeqoFHgYJuMLmd+9170EYmcQunKfgRH8UylIKjHXmsj/CAeavxOBtUqm7NXYiuAiugSgo1B5XP/jARWQQxCsWN8Zibop9zjVIomJX7mYGUiwkfgWcx5hEYP1+sPKPnYaIpjoEu3r+zOY+MmUaBzUQcx2bZmw//87wMwxs/l3GaIcTCRqwXZopiQufN6VBqEKimFrjQ0m5JxZhrLtDep2zrs+Wyq9C5rDG3xu6uqnVWHKJETskZuSCMXJM6aZAmaRNBEvJM3si7EztPzovz+hNdc4o/J+SPnI9vMFmOzA==</latexit>

10THz<latexit sha1_base64="DqCwIgQuirh/c8K9XSlH94Pb78k=">AAAB7XicbZDNSsNAFIUn/tb6V3XpZrAIrkoigi4Lbrqs0D9oQplMb9qhk0yYuRFr6GPoStSdL+ML+DZOaxbaelbf3HMG7rlhKoVB1/1y1tY3Nre2Szvl3b39g8PK0XHHqExzaHMlle6FzIAUCbRRoIReqoHFoYRuOLmd+9170EaopIXTFIKYjRIRCc7QjnzP9REeMG81HmeDStWtuQvRVfAKqJJCzUHl0x8qnsWQIJfMmL7nphjkTKPgEmZlPzOQMj5hI+hbTFgMJsgXO8/oeaQ0xTHQxft3NmexMdM4tJmY4dgse/Phf14/w+gmyEWSZggJtxHrRZmkqOi8Oh0KDRzl1ALjWtgtKR8zzTjaA5VtfW+57Cp0LmueW/Purqp1rzhEiZySM3JBPHJN6qRBmqRNOEnJM3kj745ynpwX5/UnuuYUf07IHzkf3578jwY=</latexit><latexit sha1_base64="DqCwIgQuirh/c8K9XSlH94Pb78k=">AAAB7XicbZDNSsNAFIUn/tb6V3XpZrAIrkoigi4Lbrqs0D9oQplMb9qhk0yYuRFr6GPoStSdL+ML+DZOaxbaelbf3HMG7rlhKoVB1/1y1tY3Nre2Szvl3b39g8PK0XHHqExzaHMlle6FzIAUCbRRoIReqoHFoYRuOLmd+9170EaopIXTFIKYjRIRCc7QjnzP9REeMG81HmeDStWtuQvRVfAKqJJCzUHl0x8qnsWQIJfMmL7nphjkTKPgEmZlPzOQMj5hI+hbTFgMJsgXO8/oeaQ0xTHQxft3NmexMdM4tJmY4dgse/Phf14/w+gmyEWSZggJtxHrRZmkqOi8Oh0KDRzl1ALjWtgtKR8zzTjaA5VtfW+57Cp0LmueW/Purqp1rzhEiZySM3JBPHJN6qRBmqRNOEnJM3kj745ynpwX5/UnuuYUf07IHzkf3578jwY=</latexit><latexit sha1_base64="DqCwIgQuirh/c8K9XSlH94Pb78k=">AAAB7XicbZDNSsNAFIUn/tb6V3XpZrAIrkoigi4Lbrqs0D9oQplMb9qhk0yYuRFr6GPoStSdL+ML+DZOaxbaelbf3HMG7rlhKoVB1/1y1tY3Nre2Szvl3b39g8PK0XHHqExzaHMlle6FzIAUCbRRoIReqoHFoYRuOLmd+9170EaopIXTFIKYjRIRCc7QjnzP9REeMG81HmeDStWtuQvRVfAKqJJCzUHl0x8qnsWQIJfMmL7nphjkTKPgEmZlPzOQMj5hI+hbTFgMJsgXO8/oeaQ0xTHQxft3NmexMdM4tJmY4dgse/Phf14/w+gmyEWSZggJtxHrRZmkqOi8Oh0KDRzl1ALjWtgtKR8zzTjaA5VtfW+57Cp0LmueW/Purqp1rzhEiZySM3JBPHJN6qRBmqRNOEnJM3kj745ynpwX5/UnuuYUf07IHzkf3578jwY=</latexit><latexit sha1_base64="DqCwIgQuirh/c8K9XSlH94Pb78k=">AAAB7XicbZDNSsNAFIUn/tb6V3XpZrAIrkoigi4Lbrqs0D9oQplMb9qhk0yYuRFr6GPoStSdL+ML+DZOaxbaelbf3HMG7rlhKoVB1/1y1tY3Nre2Szvl3b39g8PK0XHHqExzaHMlle6FzIAUCbRRoIReqoHFoYRuOLmd+9170EaopIXTFIKYjRIRCc7QjnzP9REeMG81HmeDStWtuQvRVfAKqJJCzUHl0x8qnsWQIJfMmL7nphjkTKPgEmZlPzOQMj5hI+hbTFgMJsgXO8/oeaQ0xTHQxft3NmexMdM4tJmY4dgse/Phf14/w+gmyEWSZggJtxHrRZmkqOi8Oh0KDRzl1ALjWtgtKR8zzTjaA5VtfW+57Cp0LmueW/Purqp1rzhEiZySM3JBPHJN6qRBmqRNOEnJM3kj745ynpwX5/UnuuYUf07IHzkf3578jwY=</latexit>

100THz<latexit sha1_base64="Yh/KE+bntYbelm0a96sr2QwCtLk=">AAAB7nicbZDLTgIxFIY7eEO8oS7dTCQmrkhrTHRJ4oYlJtwSmJBOOQMNnYvtGSNOeA1dGXXnw/gCvo0FZ6Hgv/p6/r/J+Y+fKGmQ0i+nsLa+sblV3C7t7O7tH5QPj9omTrWAlohVrLs+N6BkBC2UqKCbaOChr6DjT27mfucetJFx1MRpAl7IR5EMpOBoRx6jtI/wgFmz/jgblCu0ShdyV4HlUCG5GoPyZ38YizSECIXixvQYTdDLuEYpFMxK/dRAwsWEj6BnMeIhGC9bLD1zz4JYuzgGd/H+nc14aMw09G0m5Dg2y958+J/XSzG49jIZJSlCJGzEekGqXIzdeXd3KDUIVFMLXGhpt3TFmGsu0F6oZOuz5bKr0L6oMlplt5eVGssPUSQn5JScE0auSI3USYO0iCB35Jm8kXcncZ6cF+f1J1pw8j/H5I+cj28N4I9A</latexit><latexit sha1_base64="Yh/KE+bntYbelm0a96sr2QwCtLk=">AAAB7nicbZDLTgIxFIY7eEO8oS7dTCQmrkhrTHRJ4oYlJtwSmJBOOQMNnYvtGSNOeA1dGXXnw/gCvo0FZ6Hgv/p6/r/J+Y+fKGmQ0i+nsLa+sblV3C7t7O7tH5QPj9omTrWAlohVrLs+N6BkBC2UqKCbaOChr6DjT27mfucetJFx1MRpAl7IR5EMpOBoRx6jtI/wgFmz/jgblCu0ShdyV4HlUCG5GoPyZ38YizSECIXixvQYTdDLuEYpFMxK/dRAwsWEj6BnMeIhGC9bLD1zz4JYuzgGd/H+nc14aMw09G0m5Dg2y958+J/XSzG49jIZJSlCJGzEekGqXIzdeXd3KDUIVFMLXGhpt3TFmGsu0F6oZOuz5bKr0L6oMlplt5eVGssPUSQn5JScE0auSI3USYO0iCB35Jm8kXcncZ6cF+f1J1pw8j/H5I+cj28N4I9A</latexit><latexit sha1_base64="Yh/KE+bntYbelm0a96sr2QwCtLk=">AAAB7nicbZDLTgIxFIY7eEO8oS7dTCQmrkhrTHRJ4oYlJtwSmJBOOQMNnYvtGSNOeA1dGXXnw/gCvo0FZ6Hgv/p6/r/J+Y+fKGmQ0i+nsLa+sblV3C7t7O7tH5QPj9omTrWAlohVrLs+N6BkBC2UqKCbaOChr6DjT27mfucetJFx1MRpAl7IR5EMpOBoRx6jtI/wgFmz/jgblCu0ShdyV4HlUCG5GoPyZ38YizSECIXixvQYTdDLuEYpFMxK/dRAwsWEj6BnMeIhGC9bLD1zz4JYuzgGd/H+nc14aMw09G0m5Dg2y958+J/XSzG49jIZJSlCJGzEekGqXIzdeXd3KDUIVFMLXGhpt3TFmGsu0F6oZOuz5bKr0L6oMlplt5eVGssPUSQn5JScE0auSI3USYO0iCB35Jm8kXcncZ6cF+f1J1pw8j/H5I+cj28N4I9A</latexit><latexit sha1_base64="Yh/KE+bntYbelm0a96sr2QwCtLk=">AAAB7nicbZDLTgIxFIY7eEO8oS7dTCQmrkhrTHRJ4oYlJtwSmJBOOQMNnYvtGSNOeA1dGXXnw/gCvo0FZ6Hgv/p6/r/J+Y+fKGmQ0i+nsLa+sblV3C7t7O7tH5QPj9omTrWAlohVrLs+N6BkBC2UqKCbaOChr6DjT27mfucetJFx1MRpAl7IR5EMpOBoRx6jtI/wgFmz/jgblCu0ShdyV4HlUCG5GoPyZ38YizSECIXixvQYTdDLuEYpFMxK/dRAwsWEj6BnMeIhGC9bLD1zz4JYuzgGd/H+nc14aMw09G0m5Dg2y958+J/XSzG49jIZJSlCJGzEekGqXIzdeXd3KDUIVFMLXGhpt3TFmGsu0F6oZOuz5bKr0L6oMlplt5eVGssPUSQn5JScE0auSI3USYO0iCB35Jm8kXcncZ6cF+f1J1pw8j/H5I+cj28N4I9A</latexit>

1PHz<latexit sha1_base64="NW+l4X4jfImeOELUjJb2SCgc+H8=">AAAB7HicbZDLSgMxFIYz9VbrrerSTbAIrspEBF0W3HRZwV5gOpRMeqYNzVxIzoh16FvoStSdT+ML+DamdRba+q++nP8PnP8EqZIGXffLKa2tb2xulbcrO7t7+wfVw6OOSTItoC0SlehewA0oGUMbJSropRp4FCjoBpObud+9B21kEt/hNAU/4qNYhlJwtCOP9REeMG81H2eDas2tuwvRVWAF1Eih1qD62R8mIosgRqG4MR5zU/RzrlEKBbNKPzOQcjHhI/AsxjwC4+eLlWf0LEw0xTHQxft3NueRMdMosJmI49gse/Phf56XYXjt5zJOM4RY2Ij1wkxRTOi8OR1KDQLV1AIXWtotqRhzzQXa+1RsfbZcdhU6F3Xm1tntZa3BikOUyQk5JeeEkSvSIE3SIm0iSEKeyRt5d2LnyXlxXn+iJaf4c0z+yPn4BipVjsg=</latexit><latexit sha1_base64="NW+l4X4jfImeOELUjJb2SCgc+H8=">AAAB7HicbZDLSgMxFIYz9VbrrerSTbAIrspEBF0W3HRZwV5gOpRMeqYNzVxIzoh16FvoStSdT+ML+DamdRba+q++nP8PnP8EqZIGXffLKa2tb2xulbcrO7t7+wfVw6OOSTItoC0SlehewA0oGUMbJSropRp4FCjoBpObud+9B21kEt/hNAU/4qNYhlJwtCOP9REeMG81H2eDas2tuwvRVWAF1Eih1qD62R8mIosgRqG4MR5zU/RzrlEKBbNKPzOQcjHhI/AsxjwC4+eLlWf0LEw0xTHQxft3NueRMdMosJmI49gse/Phf56XYXjt5zJOM4RY2Ij1wkxRTOi8OR1KDQLV1AIXWtotqRhzzQXa+1RsfbZcdhU6F3Xm1tntZa3BikOUyQk5JeeEkSvSIE3SIm0iSEKeyRt5d2LnyXlxXn+iJaf4c0z+yPn4BipVjsg=</latexit><latexit sha1_base64="NW+l4X4jfImeOELUjJb2SCgc+H8=">AAAB7HicbZDLSgMxFIYz9VbrrerSTbAIrspEBF0W3HRZwV5gOpRMeqYNzVxIzoh16FvoStSdT+ML+DamdRba+q++nP8PnP8EqZIGXffLKa2tb2xulbcrO7t7+wfVw6OOSTItoC0SlehewA0oGUMbJSropRp4FCjoBpObud+9B21kEt/hNAU/4qNYhlJwtCOP9REeMG81H2eDas2tuwvRVWAF1Eih1qD62R8mIosgRqG4MR5zU/RzrlEKBbNKPzOQcjHhI/AsxjwC4+eLlWf0LEw0xTHQxft3NueRMdMosJmI49gse/Phf56XYXjt5zJOM4RY2Ij1wkxRTOi8OR1KDQLV1AIXWtotqRhzzQXa+1RsfbZcdhU6F3Xm1tntZa3BikOUyQk5JeeEkSvSIE3SIm0iSEKeyRt5d2LnyXlxXn+iJaf4c0z+yPn4BipVjsg=</latexit><latexit sha1_base64="NW+l4X4jfImeOELUjJb2SCgc+H8=">AAAB7HicbZDLSgMxFIYz9VbrrerSTbAIrspEBF0W3HRZwV5gOpRMeqYNzVxIzoh16FvoStSdT+ML+DamdRba+q++nP8PnP8EqZIGXffLKa2tb2xulbcrO7t7+wfVw6OOSTItoC0SlehewA0oGUMbJSropRp4FCjoBpObud+9B21kEt/hNAU/4qNYhlJwtCOP9REeMG81H2eDas2tuwvRVWAF1Eih1qD62R8mIosgRqG4MR5zU/RzrlEKBbNKPzOQcjHhI/AsxjwC4+eLlWf0LEw0xTHQxft3NueRMdMosJmI49gse/Phf56XYXjt5zJOM4RY2Ij1wkxRTOi8OR1KDQLV1AIXWtotqRhzzQXa+1RsfbZcdhU6F3Xm1tntZa3BikOUyQk5JeeEkSvSIE3SIm0iSEKeyRt5d2LnyXlxXn+iJaf4c0z+yPn4BipVjsg=</latexit>

102<latexit sha1_base64="Ln0VrmyLtQSPnMLkbOncEks6y1g=">AAAB6HicbZDLTgIxFIbP4A3xhrp000hM3EimhESXJG5cYiKXBEbSKWeg0rmk7ZiQCe+gK6PufB5fwLex4CwU/Fdfz/83Of/xEym0cd0vp7C2vrG5Vdwu7ezu7R+UD4/aOk4VxxaPZay6PtMoRYQtI4zEbqKQhb7Ejj+5nvudR1RaxNGdmSbohWwUiUBwZuyoQ9377KI2G5QrbtVdiKwCzaECuZqD8md/GPM0xMhwybTuUTcxXsaUEVzirNRPNSaMT9gIexYjFqL2ssW6M3IWxIqYMZLF+3c2Y6HW09C3mZCZsV725sP/vF5qgisvE1GSGoy4jVgvSCUxMZm3JkOhkBs5tcC4EnZLwsdMMW7sbUq2Pl0uuwrtWpW6VXpbrzRofoginMApnAOFS2jADTShBRwm8Axv8O48OE/Oi/P6Ey04+Z9j+CPn4xsi+Yxa</latexit><latexit sha1_base64="Ln0VrmyLtQSPnMLkbOncEks6y1g=">AAAB6HicbZDLTgIxFIbP4A3xhrp000hM3EimhESXJG5cYiKXBEbSKWeg0rmk7ZiQCe+gK6PufB5fwLex4CwU/Fdfz/83Of/xEym0cd0vp7C2vrG5Vdwu7ezu7R+UD4/aOk4VxxaPZay6PtMoRYQtI4zEbqKQhb7Ejj+5nvudR1RaxNGdmSbohWwUiUBwZuyoQ9377KI2G5QrbtVdiKwCzaECuZqD8md/GPM0xMhwybTuUTcxXsaUEVzirNRPNSaMT9gIexYjFqL2ssW6M3IWxIqYMZLF+3c2Y6HW09C3mZCZsV725sP/vF5qgisvE1GSGoy4jVgvSCUxMZm3JkOhkBs5tcC4EnZLwsdMMW7sbUq2Pl0uuwrtWpW6VXpbrzRofoginMApnAOFS2jADTShBRwm8Axv8O48OE/Oi/P6Ey04+Z9j+CPn4xsi+Yxa</latexit><latexit sha1_base64="Ln0VrmyLtQSPnMLkbOncEks6y1g=">AAAB6HicbZDLTgIxFIbP4A3xhrp000hM3EimhESXJG5cYiKXBEbSKWeg0rmk7ZiQCe+gK6PufB5fwLex4CwU/Fdfz/83Of/xEym0cd0vp7C2vrG5Vdwu7ezu7R+UD4/aOk4VxxaPZay6PtMoRYQtI4zEbqKQhb7Ejj+5nvudR1RaxNGdmSbohWwUiUBwZuyoQ9377KI2G5QrbtVdiKwCzaECuZqD8md/GPM0xMhwybTuUTcxXsaUEVzirNRPNSaMT9gIexYjFqL2ssW6M3IWxIqYMZLF+3c2Y6HW09C3mZCZsV725sP/vF5qgisvE1GSGoy4jVgvSCUxMZm3JkOhkBs5tcC4EnZLwsdMMW7sbUq2Pl0uuwrtWpW6VXpbrzRofoginMApnAOFS2jADTShBRwm8Axv8O48OE/Oi/P6Ey04+Z9j+CPn4xsi+Yxa</latexit><latexit sha1_base64="Ln0VrmyLtQSPnMLkbOncEks6y1g=">AAAB6HicbZDLTgIxFIbP4A3xhrp000hM3EimhESXJG5cYiKXBEbSKWeg0rmk7ZiQCe+gK6PufB5fwLex4CwU/Fdfz/83Of/xEym0cd0vp7C2vrG5Vdwu7ezu7R+UD4/aOk4VxxaPZay6PtMoRYQtI4zEbqKQhb7Ejj+5nvudR1RaxNGdmSbohWwUiUBwZuyoQ9377KI2G5QrbtVdiKwCzaECuZqD8md/GPM0xMhwybTuUTcxXsaUEVzirNRPNSaMT9gIexYjFqL2ssW6M3IWxIqYMZLF+3c2Y6HW09C3mZCZsV725sP/vF5qgisvE1GSGoy4jVgvSCUxMZm3JkOhkBs5tcC4EnZLwsdMMW7sbUq2Pl0uuwrtWpW6VXpbrzRofoginMApnAOFS2jADTShBRwm8Axv8O48OE/Oi/P6Ey04+Z9j+CPn4xsi+Yxa</latexit>

101<latexit sha1_base64="5jLEY4Fa6tWzWimfoHOoSZDbOfE=">AAAB6HicbZDLSgMxFIbP1Futt6pLN8EiuLFMRNBlwY3LCvYC7Vgy6Zk2NnMhyQhlmHfQlag7n8cX8G1M6yy09V99Of8fOP/xEym0cd0vp7Syura+Ud6sbG3v7O5V9w/aOk4VxxaPZay6PtMoRYQtI4zEbqKQhb7Ejj+5nvmdR1RaxNGdmSbohWwUiUBwZuyoQ9377Izmg2rNrbtzkWWgBdSgUHNQ/ewPY56GGBkumdY96ibGy5gygkvMK/1UY8L4hI2wZzFiIWovm6+bk5MgVsSMkczfv7MZC7Wehr7NhMyM9aI3G/7n9VITXHmZiJLUYMRtxHpBKomJyaw1GQqF3MipBcaVsFsSPmaKcWNvU7H16WLZZWif16lbp7cXtQYtDlGGIziGU6BwCQ24gSa0gMMEnuEN3p0H58l5cV5/oiWn+HMIf+R8fAMheoxZ</latexit><latexit sha1_base64="5jLEY4Fa6tWzWimfoHOoSZDbOfE=">AAAB6HicbZDLSgMxFIbP1Futt6pLN8EiuLFMRNBlwY3LCvYC7Vgy6Zk2NnMhyQhlmHfQlag7n8cX8G1M6yy09V99Of8fOP/xEym0cd0vp7Syura+Ud6sbG3v7O5V9w/aOk4VxxaPZay6PtMoRYQtI4zEbqKQhb7Ejj+5nvmdR1RaxNGdmSbohWwUiUBwZuyoQ9377Izmg2rNrbtzkWWgBdSgUHNQ/ewPY56GGBkumdY96ibGy5gygkvMK/1UY8L4hI2wZzFiIWovm6+bk5MgVsSMkczfv7MZC7Wehr7NhMyM9aI3G/7n9VITXHmZiJLUYMRtxHpBKomJyaw1GQqF3MipBcaVsFsSPmaKcWNvU7H16WLZZWif16lbp7cXtQYtDlGGIziGU6BwCQ24gSa0gMMEnuEN3p0H58l5cV5/oiWn+HMIf+R8fAMheoxZ</latexit><latexit sha1_base64="5jLEY4Fa6tWzWimfoHOoSZDbOfE=">AAAB6HicbZDLSgMxFIbP1Futt6pLN8EiuLFMRNBlwY3LCvYC7Vgy6Zk2NnMhyQhlmHfQlag7n8cX8G1M6yy09V99Of8fOP/xEym0cd0vp7Syura+Ud6sbG3v7O5V9w/aOk4VxxaPZay6PtMoRYQtI4zEbqKQhb7Ejj+5nvmdR1RaxNGdmSbohWwUiUBwZuyoQ9377Izmg2rNrbtzkWWgBdSgUHNQ/ewPY56GGBkumdY96ibGy5gygkvMK/1UY8L4hI2wZzFiIWovm6+bk5MgVsSMkczfv7MZC7Wehr7NhMyM9aI3G/7n9VITXHmZiJLUYMRtxHpBKomJyaw1GQqF3MipBcaVsFsSPmaKcWNvU7H16WLZZWif16lbp7cXtQYtDlGGIziGU6BwCQ24gSa0gMMEnuEN3p0H58l5cV5/oiWn+HMIf+R8fAMheoxZ</latexit><latexit sha1_base64="5jLEY4Fa6tWzWimfoHOoSZDbOfE=">AAAB6HicbZDLSgMxFIbP1Futt6pLN8EiuLFMRNBlwY3LCvYC7Vgy6Zk2NnMhyQhlmHfQlag7n8cX8G1M6yy09V99Of8fOP/xEym0cd0vp7Syura+Ud6sbG3v7O5V9w/aOk4VxxaPZay6PtMoRYQtI4zEbqKQhb7Ejj+5nvmdR1RaxNGdmSbohWwUiUBwZuyoQ9377Izmg2rNrbtzkWWgBdSgUHNQ/ewPY56GGBkumdY96ibGy5gygkvMK/1UY8L4hI2wZzFiIWovm6+bk5MgVsSMkczfv7MZC7Wehr7NhMyM9aI3G/7n9VITXHmZiJLUYMRtxHpBKomJyaw1GQqF3MipBcaVsFsSPmaKcWNvU7H16WLZZWif16lbp7cXtQYtDlGGIziGU6BwCQ24gSa0gMMEnuEN3p0H58l5cV5/oiWn+HMIf+R8fAMheoxZ</latexit>

1<latexit sha1_base64="2nVcxP2yHnvgKz2+4oF9WVNze24=">AAAB4nicbZDNSgMxFIXv1L9a/6ou3QSL4KpMRNBlwY3LFuwPtEPJpHfa0ExmSDJCGfoCuhJ15yP5Ar6NaZ2Ftp7Vl3tO4J4bplIY6/tfXmljc2t7p7xb2ds/ODyqHp90TJJpjm2eyET3QmZQCoVtK6zEXqqRxaHEbji9W/jdR9RGJOrBzlIMYjZWIhKcWTdq0WG15tf9pcg60AJqUKg5rH4ORgnPYlSWS2ZMn/qpDXKmreAS55VBZjBlfMrG2HeoWIwmyJeLzslFlGhiJ0iW79/ZnMXGzOLQZWJmJ2bVWwz/8/qZjW6DXKg0s6i4izgvyiSxCVn0JSOhkVs5c8C4Fm5LwidMM27dVSquPl0tuw6dqzr167R1XWvQ4hBlOINzuAQKN9CAe2hCGzggPMMbvHsj78l78V5/oiWv+HMKf+R9fANsKoo5</latexit><latexit sha1_base64="2nVcxP2yHnvgKz2+4oF9WVNze24=">AAAB4nicbZDNSgMxFIXv1L9a/6ou3QSL4KpMRNBlwY3LFuwPtEPJpHfa0ExmSDJCGfoCuhJ15yP5Ar6NaZ2Ftp7Vl3tO4J4bplIY6/tfXmljc2t7p7xb2ds/ODyqHp90TJJpjm2eyET3QmZQCoVtK6zEXqqRxaHEbji9W/jdR9RGJOrBzlIMYjZWIhKcWTdq0WG15tf9pcg60AJqUKg5rH4ORgnPYlSWS2ZMn/qpDXKmreAS55VBZjBlfMrG2HeoWIwmyJeLzslFlGhiJ0iW79/ZnMXGzOLQZWJmJ2bVWwz/8/qZjW6DXKg0s6i4izgvyiSxCVn0JSOhkVs5c8C4Fm5LwidMM27dVSquPl0tuw6dqzr167R1XWvQ4hBlOINzuAQKN9CAe2hCGzggPMMbvHsj78l78V5/oiWv+HMKf+R9fANsKoo5</latexit><latexit sha1_base64="2nVcxP2yHnvgKz2+4oF9WVNze24=">AAAB4nicbZDNSgMxFIXv1L9a/6ou3QSL4KpMRNBlwY3LFuwPtEPJpHfa0ExmSDJCGfoCuhJ15yP5Ar6NaZ2Ftp7Vl3tO4J4bplIY6/tfXmljc2t7p7xb2ds/ODyqHp90TJJpjm2eyET3QmZQCoVtK6zEXqqRxaHEbji9W/jdR9RGJOrBzlIMYjZWIhKcWTdq0WG15tf9pcg60AJqUKg5rH4ORgnPYlSWS2ZMn/qpDXKmreAS55VBZjBlfMrG2HeoWIwmyJeLzslFlGhiJ0iW79/ZnMXGzOLQZWJmJ2bVWwz/8/qZjW6DXKg0s6i4izgvyiSxCVn0JSOhkVs5c8C4Fm5LwidMM27dVSquPl0tuw6dqzr167R1XWvQ4hBlOINzuAQKN9CAe2hCGzggPMMbvHsj78l78V5/oiWv+HMKf+R9fANsKoo5</latexit><latexit sha1_base64="2nVcxP2yHnvgKz2+4oF9WVNze24=">AAAB4nicbZDNSgMxFIXv1L9a/6ou3QSL4KpMRNBlwY3LFuwPtEPJpHfa0ExmSDJCGfoCuhJ15yP5Ar6NaZ2Ftp7Vl3tO4J4bplIY6/tfXmljc2t7p7xb2ds/ODyqHp90TJJpjm2eyET3QmZQCoVtK6zEXqqRxaHEbji9W/jdR9RGJOrBzlIMYjZWIhKcWTdq0WG15tf9pcg60AJqUKg5rH4ORgnPYlSWS2ZMn/qpDXKmreAS55VBZjBlfMrG2HeoWIwmyJeLzslFlGhiJ0iW79/ZnMXGzOLQZWJmJ2bVWwz/8/qZjW6DXKg0s6i4izgvyiSxCVn0JSOhkVs5c8C4Fm5LwidMM27dVSquPl0tuw6dqzr167R1XWvQ4hBlOINzuAQKN9CAe2hCGzggPMMbvHsj78l78V5/oiWv+HMKf+R9fANsKoo5</latexit>

10<latexit sha1_base64="kD28XM6EULZjv2wYPIY2dGmaAVI=">AAAB43icbZDLSgMxFIZP6q3WW9Wlm2ARXJWJCLosuHFZxV6gHUomPdOGZi4kGaEMfQJdibrzjXwB38a0zkJb/9WX8/+B858gVdJYz/sipbX1jc2t8nZlZ3dv/6B6eNQ2SaYFtkSiEt0NuEElY2xZaRV2U408ChR2gsnN3O88ojYyiR/sNEU/4qNYhlJw60b3zBtUa17dW4iuAiugBoWag+pnf5iILMLYCsWN6TEvtX7OtZVC4azSzwymXEz4CHsOYx6h8fPFpjN6Fiaa2jHSxft3NueRMdMocJmI27FZ9ubD/7xeZsNrP5dxmlmMhYs4L8wUtQmdF6ZDqVFYNXXAhZZuSyrGXHNh3Vkqrj5bLrsK7Ys68+rs7rLWYMUhynACp3AODK6gAbfQhBYICOEZ3uCdIHkiL+T1J1oixZ9j+CPy8Q3Y2Ypz</latexit><latexit sha1_base64="kD28XM6EULZjv2wYPIY2dGmaAVI=">AAAB43icbZDLSgMxFIZP6q3WW9Wlm2ARXJWJCLosuHFZxV6gHUomPdOGZi4kGaEMfQJdibrzjXwB38a0zkJb/9WX8/+B858gVdJYz/sipbX1jc2t8nZlZ3dv/6B6eNQ2SaYFtkSiEt0NuEElY2xZaRV2U408ChR2gsnN3O88ojYyiR/sNEU/4qNYhlJw60b3zBtUa17dW4iuAiugBoWag+pnf5iILMLYCsWN6TEvtX7OtZVC4azSzwymXEz4CHsOYx6h8fPFpjN6Fiaa2jHSxft3NueRMdMocJmI27FZ9ubD/7xeZsNrP5dxmlmMhYs4L8wUtQmdF6ZDqVFYNXXAhZZuSyrGXHNh3Vkqrj5bLrsK7Ys68+rs7rLWYMUhynACp3AODK6gAbfQhBYICOEZ3uCdIHkiL+T1J1oixZ9j+CPy8Q3Y2Ypz</latexit><latexit sha1_base64="kD28XM6EULZjv2wYPIY2dGmaAVI=">AAAB43icbZDLSgMxFIZP6q3WW9Wlm2ARXJWJCLosuHFZxV6gHUomPdOGZi4kGaEMfQJdibrzjXwB38a0zkJb/9WX8/+B858gVdJYz/sipbX1jc2t8nZlZ3dv/6B6eNQ2SaYFtkSiEt0NuEElY2xZaRV2U408ChR2gsnN3O88ojYyiR/sNEU/4qNYhlJw60b3zBtUa17dW4iuAiugBoWag+pnf5iILMLYCsWN6TEvtX7OtZVC4azSzwymXEz4CHsOYx6h8fPFpjN6Fiaa2jHSxft3NueRMdMocJmI27FZ9ubD/7xeZsNrP5dxmlmMhYs4L8wUtQmdF6ZDqVFYNXXAhZZuSyrGXHNh3Vkqrj5bLrsK7Ys68+rs7rLWYMUhynACp3AODK6gAbfQhBYICOEZ3uCdIHkiL+T1J1oixZ9j+CPy8Q3Y2Ypz</latexit><latexit sha1_base64="kD28XM6EULZjv2wYPIY2dGmaAVI=">AAAB43icbZDLSgMxFIZP6q3WW9Wlm2ARXJWJCLosuHFZxV6gHUomPdOGZi4kGaEMfQJdibrzjXwB38a0zkJb/9WX8/+B858gVdJYz/sipbX1jc2t8nZlZ3dv/6B6eNQ2SaYFtkSiEt0NuEElY2xZaRV2U408ChR2gsnN3O88ojYyiR/sNEU/4qNYhlJw60b3zBtUa17dW4iuAiugBoWag+pnf5iILMLYCsWN6TEvtX7OtZVC4azSzwymXEz4CHsOYx6h8fPFpjN6Fiaa2jHSxft3NueRMdMocJmI27FZ9ubD/7xeZsNrP5dxmlmMhYs4L8wUtQmdF6ZDqVFYNXXAhZZuSyrGXHNh3Vkqrj5bLrsK7Ys68+rs7rLWYMUhynACp3AODK6gAbfQhBYICOEZ3uCdIHkiL+T1J1oixZ9j+CPy8Q3Y2Ypz</latexit>

102<latexit sha1_base64="pPU84OR0x6CmqAe1sXLNO9Nk4YQ=">AAAB5XicbZDLSgMxFIbPeK31VnXpJlgEV2VSBF0W3LisYC/QjiWTnumEZi4kGaEMfQRdibrzhXwB38ZMnYW2/qsv5/8D5z9+KoU2rvvlrK1vbG5tV3aqu3v7B4e1o+OuTjLFscMTmai+zzRKEWPHCCOxnypkkS+x509vCr/3iEqLJL43sxS9iE1iEQjOTDGi7kNzVKu7DXchsgq0hDqUao9qn8NxwrMIY8Ml03pA3dR4OVNGcInz6jDTmDI+ZRMcWIxZhNrLF7vOyXmQKGJCJIv372zOIq1nkW8zETOhXvaK4X/eIDPBtZeLOM0MxtxGrBdkkpiEFJXJWCjkRs4sMK6E3ZLwkCnGjT1M1dany2VXodtsULdB7y7rLVoeogKncAYXQOEKWnALbegAhxCe4Q3enYnz5Lw4rz/RNaf8cwJ/5Hx8A/qqixc=</latexit><latexit sha1_base64="pPU84OR0x6CmqAe1sXLNO9Nk4YQ=">AAAB5XicbZDLSgMxFIbPeK31VnXpJlgEV2VSBF0W3LisYC/QjiWTnumEZi4kGaEMfQRdibrzhXwB38ZMnYW2/qsv5/8D5z9+KoU2rvvlrK1vbG5tV3aqu3v7B4e1o+OuTjLFscMTmai+zzRKEWPHCCOxnypkkS+x509vCr/3iEqLJL43sxS9iE1iEQjOTDGi7kNzVKu7DXchsgq0hDqUao9qn8NxwrMIY8Ml03pA3dR4OVNGcInz6jDTmDI+ZRMcWIxZhNrLF7vOyXmQKGJCJIv372zOIq1nkW8zETOhXvaK4X/eIDPBtZeLOM0MxtxGrBdkkpiEFJXJWCjkRs4sMK6E3ZLwkCnGjT1M1dany2VXodtsULdB7y7rLVoeogKncAYXQOEKWnALbegAhxCe4Q3enYnz5Lw4rz/RNaf8cwJ/5Hx8A/qqixc=</latexit><latexit sha1_base64="pPU84OR0x6CmqAe1sXLNO9Nk4YQ=">AAAB5XicbZDLSgMxFIbPeK31VnXpJlgEV2VSBF0W3LisYC/QjiWTnumEZi4kGaEMfQRdibrzhXwB38ZMnYW2/qsv5/8D5z9+KoU2rvvlrK1vbG5tV3aqu3v7B4e1o+OuTjLFscMTmai+zzRKEWPHCCOxnypkkS+x509vCr/3iEqLJL43sxS9iE1iEQjOTDGi7kNzVKu7DXchsgq0hDqUao9qn8NxwrMIY8Ml03pA3dR4OVNGcInz6jDTmDI+ZRMcWIxZhNrLF7vOyXmQKGJCJIv372zOIq1nkW8zETOhXvaK4X/eIDPBtZeLOM0MxtxGrBdkkpiEFJXJWCjkRs4sMK6E3ZLwkCnGjT1M1dany2VXodtsULdB7y7rLVoeogKncAYXQOEKWnALbegAhxCe4Q3enYnz5Lw4rz/RNaf8cwJ/5Hx8A/qqixc=</latexit><latexit sha1_base64="pPU84OR0x6CmqAe1sXLNO9Nk4YQ=">AAAB5XicbZDLSgMxFIbPeK31VnXpJlgEV2VSBF0W3LisYC/QjiWTnumEZi4kGaEMfQRdibrzhXwB38ZMnYW2/qsv5/8D5z9+KoU2rvvlrK1vbG5tV3aqu3v7B4e1o+OuTjLFscMTmai+zzRKEWPHCCOxnypkkS+x509vCr/3iEqLJL43sxS9iE1iEQjOTDGi7kNzVKu7DXchsgq0hDqUao9qn8NxwrMIY8Ml03pA3dR4OVNGcInz6jDTmDI+ZRMcWIxZhNrLF7vOyXmQKGJCJIv372zOIq1nkW8zETOhXvaK4X/eIDPBtZeLOM0MxtxGrBdkkpiEFJXJWCjkRs4sMK6E3ZLwkCnGjT1M1dany2VXodtsULdB7y7rLVoeogKncAYXQOEKWnALbegAhxCe4Q3enYnz5Lw4rz/RNaf8cwJ/5Hx8A/qqixc=</latexit>

103<latexit sha1_base64="Xt5vYVpXhtjg77d/r3TOOE8hogs=">AAAB5XicbZDLSgMxFIbPeK31VnXpJlgEV2Wigi4LblxWsBdox5JJz3RCMxeSjFCGPoKuRN35Qr6Ab2OmzkJb/9WX8/+B8x8/lUIb1/1yVlbX1jc2K1vV7Z3dvf3awWFHJ5ni2OaJTFTPZxqliLFthJHYSxWyyJfY9Sc3hd99RKVFEt+baYpexMaxCARnphhR9+FiWKu7DXcusgy0hDqUag1rn4NRwrMIY8Ml07pP3dR4OVNGcImz6iDTmDI+YWPsW4xZhNrL57vOyGmQKGJCJPP372zOIq2nkW8zETOhXvSK4X9ePzPBtZeLOM0MxtxGrBdkkpiEFJXJSCjkRk4tMK6E3ZLwkCnGjT1M1dani2WXoXPeoG6D3l3Wm7Q8RAWO4QTOgMIVNOEWWtAGDiE8wxu8O2PnyXlxXn+iK0755wj+yPn4Bvwoixg=</latexit><latexit sha1_base64="Xt5vYVpXhtjg77d/r3TOOE8hogs=">AAAB5XicbZDLSgMxFIbPeK31VnXpJlgEV2Wigi4LblxWsBdox5JJz3RCMxeSjFCGPoKuRN35Qr6Ab2OmzkJb/9WX8/+B8x8/lUIb1/1yVlbX1jc2K1vV7Z3dvf3awWFHJ5ni2OaJTFTPZxqliLFthJHYSxWyyJfY9Sc3hd99RKVFEt+baYpexMaxCARnphhR9+FiWKu7DXcusgy0hDqUag1rn4NRwrMIY8Ml07pP3dR4OVNGcImz6iDTmDI+YWPsW4xZhNrL57vOyGmQKGJCJPP372zOIq2nkW8zETOhXvSK4X9ePzPBtZeLOM0MxtxGrBdkkpiEFJXJSCjkRk4tMK6E3ZLwkCnGjT1M1dani2WXoXPeoG6D3l3Wm7Q8RAWO4QTOgMIVNOEWWtAGDiE8wxu8O2PnyXlxXn+iK0755wj+yPn4Bvwoixg=</latexit><latexit sha1_base64="Xt5vYVpXhtjg77d/r3TOOE8hogs=">AAAB5XicbZDLSgMxFIbPeK31VnXpJlgEV2Wigi4LblxWsBdox5JJz3RCMxeSjFCGPoKuRN35Qr6Ab2OmzkJb/9WX8/+B8x8/lUIb1/1yVlbX1jc2K1vV7Z3dvf3awWFHJ5ni2OaJTFTPZxqliLFthJHYSxWyyJfY9Sc3hd99RKVFEt+baYpexMaxCARnphhR9+FiWKu7DXcusgy0hDqUag1rn4NRwrMIY8Ml07pP3dR4OVNGcImz6iDTmDI+YWPsW4xZhNrL57vOyGmQKGJCJPP372zOIq2nkW8zETOhXvSK4X9ePzPBtZeLOM0MxtxGrBdkkpiEFJXJSCjkRk4tMK6E3ZLwkCnGjT1M1dani2WXoXPeoG6D3l3Wm7Q8RAWO4QTOgMIVNOEWWtAGDiE8wxu8O2PnyXlxXn+iK0755wj+yPn4Bvwoixg=</latexit><latexit sha1_base64="Xt5vYVpXhtjg77d/r3TOOE8hogs=">AAAB5XicbZDLSgMxFIbPeK31VnXpJlgEV2Wigi4LblxWsBdox5JJz3RCMxeSjFCGPoKuRN35Qr6Ab2OmzkJb/9WX8/+B8x8/lUIb1/1yVlbX1jc2K1vV7Z3dvf3awWFHJ5ni2OaJTFTPZxqliLFthJHYSxWyyJfY9Sc3hd99RKVFEt+baYpexMaxCARnphhR9+FiWKu7DXcusgy0hDqUag1rn4NRwrMIY8Ml07pP3dR4OVNGcImz6iDTmDI+YWPsW4xZhNrL57vOyGmQKGJCJPP372zOIq2nkW8zETOhXvSK4X9ePzPBtZeLOM0MxtxGrBdkkpiEFJXJSCjkRk4tMK6E3ZLwkCnGjT1M1dani2WXoXPeoG6D3l3Wm7Q8RAWO4QTOgMIVNOEWWtAGDiE8wxu8O2PnyXlxXn+iK0755wj+yPn4Bvwoixg=</latexit>

Frequency<latexit sha1_base64="BwVouWmogcznvltDLyIaNcn41yo=">AAAB83icbVDLSgNBEJyNrxhfqx69DAbBU9gVQY8BQTxGMImQLGF20kmGzD6c6QkuS75ET6Le/BN/wL9xEvegiXWq7qqGrgpTKTR63pdTWlldW98ob1a2tnd299z9g5ZOjOLQ5IlM1H3INEgRQxMFSrhPFbAolNAOx1czvT0BpUUS32GWQhCxYSwGgjO0q57rdhEeMb9W8GAg5tm051a9mjcHXSZ+QaqkQKPnfnb7CTcRxMgl07rjeykGOVMouIRppWs0pIyP2RA6lsYsAh3k88+n9GSQKIojoPP5tzdnkdZZFFpPxHCkF7XZ8j+tY3BwGeQiTg3aQNZitYGRFBM6K4D2hQKOMrOEcSXsl5SPmGIcbU0VG99fDLtMWmc136v5t+fVul8UUSZH5JicEp9ckDq5IQ3SJJxMyDN5I++OcZ6cF+f1x1pyiptD8gfOxzcZw5Ga</latexit><latexit sha1_base64="BwVouWmogcznvltDLyIaNcn41yo=">AAAB83icbVDLSgNBEJyNrxhfqx69DAbBU9gVQY8BQTxGMImQLGF20kmGzD6c6QkuS75ET6Le/BN/wL9xEvegiXWq7qqGrgpTKTR63pdTWlldW98ob1a2tnd299z9g5ZOjOLQ5IlM1H3INEgRQxMFSrhPFbAolNAOx1czvT0BpUUS32GWQhCxYSwGgjO0q57rdhEeMb9W8GAg5tm051a9mjcHXSZ+QaqkQKPnfnb7CTcRxMgl07rjeykGOVMouIRppWs0pIyP2RA6lsYsAh3k88+n9GSQKIojoPP5tzdnkdZZFFpPxHCkF7XZ8j+tY3BwGeQiTg3aQNZitYGRFBM6K4D2hQKOMrOEcSXsl5SPmGIcbU0VG99fDLtMWmc136v5t+fVul8UUSZH5JicEp9ckDq5IQ3SJJxMyDN5I++OcZ6cF+f1x1pyiptD8gfOxzcZw5Ga</latexit><latexit sha1_base64="BwVouWmogcznvltDLyIaNcn41yo=">AAAB83icbVDLSgNBEJyNrxhfqx69DAbBU9gVQY8BQTxGMImQLGF20kmGzD6c6QkuS75ET6Le/BN/wL9xEvegiXWq7qqGrgpTKTR63pdTWlldW98ob1a2tnd299z9g5ZOjOLQ5IlM1H3INEgRQxMFSrhPFbAolNAOx1czvT0BpUUS32GWQhCxYSwGgjO0q57rdhEeMb9W8GAg5tm051a9mjcHXSZ+QaqkQKPnfnb7CTcRxMgl07rjeykGOVMouIRppWs0pIyP2RA6lsYsAh3k88+n9GSQKIojoPP5tzdnkdZZFFpPxHCkF7XZ8j+tY3BwGeQiTg3aQNZitYGRFBM6K4D2hQKOMrOEcSXsl5SPmGIcbU0VG99fDLtMWmc136v5t+fVul8UUSZH5JicEp9ckDq5IQ3SJJxMyDN5I++OcZ6cF+f1x1pyiptD8gfOxzcZw5Ga</latexit><latexit sha1_base64="BwVouWmogcznvltDLyIaNcn41yo=">AAAB83icbVDLSgNBEJyNrxhfqx69DAbBU9gVQY8BQTxGMImQLGF20kmGzD6c6QkuS75ET6Le/BN/wL9xEvegiXWq7qqGrgpTKTR63pdTWlldW98ob1a2tnd299z9g5ZOjOLQ5IlM1H3INEgRQxMFSrhPFbAolNAOx1czvT0BpUUS32GWQhCxYSwGgjO0q57rdhEeMb9W8GAg5tm051a9mjcHXSZ+QaqkQKPnfnb7CTcRxMgl07rjeykGOVMouIRppWs0pIyP2RA6lsYsAh3k88+n9GSQKIojoPP5tzdnkdZZFFpPxHCkF7XZ8j+tY3BwGeQiTg3aQNZitYGRFBM6K4D2hQKOMrOEcSXsl5SPmGIcbU0VG99fDLtMWmc136v5t+fVul8UUSZH5JicEp9ckDq5IQ3SJJxMyDN5I++OcZ6cF+f1x1pyiptD8gfOxzcZw5Ga</latexit>

Att

enuat

ion

(dB

/km

)<latexit sha1_base64="3KOhzSBg4FNxRNQLk7+KFSLcyN4=">AAACDXicbVDJSgNBFOyJW4zbqEcvjUGIHuKMCApeol48RjALJCH0dF6SJj0L3W/EMMw36M/oSdSbF3/Av7GzHDSxTtVV1fCqvEgKjY7zbWUWFpeWV7KrubX1jc0te3unqsNYcajwUIaq7jENUgRQQYES6pEC5nsSat7geuTX7kFpEQZ3OIyg5bNeILqCMzRS2z5qIjxgcokIQTzWUtq8KEzUzlV6PGEDPz1s23mn6IxB54k7JXkyRbltfzU7IY99CJBLpnXDdSJsJUyh4BLSXDPWEDE+YD1oGBowH3QrGXdK6UE3VBT7QMfv39mE+VoPfc9kfIZ9PeuNxP+8Rozd81Yigig2ZbmJGK8bS4ohHU1DO0IBRzk0hHElzJWU95liHM2AOVPfnS07T6onRdcpuren+ZI7HSJL9sg+KRCXnJESuSFlUiGcPJEX8k4+rEfr2Xq13ibRjDX9s0v+wPr8AZWanF8=</latexit><latexit sha1_base64="3KOhzSBg4FNxRNQLk7+KFSLcyN4=">AAACDXicbVDJSgNBFOyJW4zbqEcvjUGIHuKMCApeol48RjALJCH0dF6SJj0L3W/EMMw36M/oSdSbF3/Av7GzHDSxTtVV1fCqvEgKjY7zbWUWFpeWV7KrubX1jc0te3unqsNYcajwUIaq7jENUgRQQYES6pEC5nsSat7geuTX7kFpEQZ3OIyg5bNeILqCMzRS2z5qIjxgcokIQTzWUtq8KEzUzlV6PGEDPz1s23mn6IxB54k7JXkyRbltfzU7IY99CJBLpnXDdSJsJUyh4BLSXDPWEDE+YD1oGBowH3QrGXdK6UE3VBT7QMfv39mE+VoPfc9kfIZ9PeuNxP+8Rozd81Yigig2ZbmJGK8bS4ohHU1DO0IBRzk0hHElzJWU95liHM2AOVPfnS07T6onRdcpuren+ZI7HSJL9sg+KRCXnJESuSFlUiGcPJEX8k4+rEfr2Xq13ibRjDX9s0v+wPr8AZWanF8=</latexit><latexit sha1_base64="3KOhzSBg4FNxRNQLk7+KFSLcyN4=">AAACDXicbVDJSgNBFOyJW4zbqEcvjUGIHuKMCApeol48RjALJCH0dF6SJj0L3W/EMMw36M/oSdSbF3/Av7GzHDSxTtVV1fCqvEgKjY7zbWUWFpeWV7KrubX1jc0te3unqsNYcajwUIaq7jENUgRQQYES6pEC5nsSat7geuTX7kFpEQZ3OIyg5bNeILqCMzRS2z5qIjxgcokIQTzWUtq8KEzUzlV6PGEDPz1s23mn6IxB54k7JXkyRbltfzU7IY99CJBLpnXDdSJsJUyh4BLSXDPWEDE+YD1oGBowH3QrGXdK6UE3VBT7QMfv39mE+VoPfc9kfIZ9PeuNxP+8Rozd81Yigig2ZbmJGK8bS4ohHU1DO0IBRzk0hHElzJWU95liHM2AOVPfnS07T6onRdcpuren+ZI7HSJL9sg+KRCXnJESuSFlUiGcPJEX8k4+rEfr2Xq13ibRjDX9s0v+wPr8AZWanF8=</latexit><latexit sha1_base64="3KOhzSBg4FNxRNQLk7+KFSLcyN4=">AAACDXicbVDJSgNBFOyJW4zbqEcvjUGIHuKMCApeol48RjALJCH0dF6SJj0L3W/EMMw36M/oSdSbF3/Av7GzHDSxTtVV1fCqvEgKjY7zbWUWFpeWV7KrubX1jc0te3unqsNYcajwUIaq7jENUgRQQYES6pEC5nsSat7geuTX7kFpEQZ3OIyg5bNeILqCMzRS2z5qIjxgcokIQTzWUtq8KEzUzlV6PGEDPz1s23mn6IxB54k7JXkyRbltfzU7IY99CJBLpnXDdSJsJUyh4BLSXDPWEDE+YD1oGBowH3QrGXdK6UE3VBT7QMfv39mE+VoPfc9kfIZ9PeuNxP+8Rozd81Yigig2ZbmJGK8bS4ohHU1DO0IBRzk0hHElzJWU95liHM2AOVPfnS07T6onRdcpuren+ZI7HSJL9sg+KRCXnJESuSFlUiGcPJEX8k4+rEfr2Xq13ibRjDX9s0v+wPr8AZWanF8=</latexit>

FIG. 2. Atmospheric attenuation (dB/km) as a function ofthe frequency (at 20C, 1 atm and 7.5 g/m3 of water). Thered dashed line at right separates visible frequencies from in-frared, while the green dashed line separates infrared frommicrowaves. The blue area corresponds to the frequenciesin which the technology of propagating quantum microwavesand superconducting circuits operates. This plot uses datataken from Ref. [28].

tectors is that a microwave photon energy is four or-ders of magnitude smaller than the energy of its opticalcounterpart. Consequently, triggering out a photocur-rent is obviously much more difficult in the microwaveregime. Additionally, traditional applications of propa-gating quantum microwaves do not make use of photode-tection. For this reason, even though there are proposalfor photodetectors from a decade ago [22–27], there areno experiments yet for propagating photons not alreadytrapped inside a cavity. To the best of our knowledge,experimental reports deal with ”gated” microwave pho-todetectors, where the time window or even the envelopeof the incoming photon is assumed to be known.

C. Advantages of Microwaves

We have previously exposed the challenges when usingquantum microwaves for quantum communication andsensing, but there are also some important advantageswhich might be worth the effort. Let us now summarizethem:

• Currently, the most advanced and promising (ac-tively developed by big companies such as Google,IBM, Intel, etc.) platform for future quantum com-puting and simulations is superconducting circuits.These typically consist of thin film layers of su-perconducting materials and Josephson junctionscomprising altogether a network of resonators andqubits. They interact precisely by means of mi-crowave photons, and the quantum state of thequbits is read out by measuring these photons.Quantum information processing occurs inside a

fridge at milikelvin temperatures, since higher tem-peratures imply additional thermal photons whichdestroy coherence. Controllability and connectiv-ity, as well as a future emergence of a quantuminternet, would suggest that distributed quantumcomputing with a local network of quantum pro-cessors must be considered [29, 30]. The use ofmicrowave-optics-microwave transduction has beensuggested but, as aforementioned, it is still not suf-ficiently efficient to date. Consequently, a directquantum communication with microwaves consti-tutes a desirable goal.

• The smaller energy associated with microwave pho-tons, which is a downside in photodetection, turnsinto an important advantage when energy con-sumption is taken into consideration.

• Atmosphere frequency-dependent losses containtwo low-opacity windows, one in the visible spec-trum, and one with even lower attenuation inthe frequency range of 100 MHz-10 GHz, as de-picted in Fig. 2. Especially under rainy conditions,microwaves are consequently a suitable frequencyrange for quantum radar and quantum communi-cation applications.

• There are important advantages of using mi-crowaves in quantum radars. There are radarsusing lower frequencies, but microwaves are con-venient for two main reasons: 1) Firstly, objectswhose size is comparable to microwave wavelength,such as vehicles, ships, and airplanes, produce largereflexions in this frequency range. The reason isthat the range resolution, i.e. the accuracy ascer-taining the distance of the target, is determined bythe bandwidth of the signal. In this consideration,from the point of view of circuit design, a lowerbandwidth is better; 2) Secondly, a narrow beam isusually required, which is afterwards used to scanaround to locate the target, but the width of thebeam is inversely proportional to the frequency ofa given antenna.

III. ROADMAP TOWARDS OPEN-AIRAPPLICATIONS

In this Section, we propose a possible roadmap oftheoretical and experimental achievements which mustbe performed in order to eventually achieve quantumcommunication and quantum illumination applicationsof propagating quantum microwaves in the near future.

A. Intra-Fridge Experiments

Taking into account the current state of the art in prop-agating quantum microwaves, the first milestone would

4

be quantum teleportation of continuous-variable quan-tum states in a fridge. There are two possibilities toattain this task, namely, making use of photodetectors,as usually performed in the optical regime [1], or em-ploying a different approach with only quadrature mea-surements [17]. Some steps in this direction have alreadybeen taken [18, 19], but there are still some intermediatestages, associated, for instance, with continuous-variablequantum state transfer. Deterministic state transferand entanglement protocols between two superconduct-ing qubits fabricated on separate chips have already beenachieved in Ref. [16], which is especially interesting fordistributed quantum computing. However, the resilienceof Fock states, when propagating in a thermal environ-ment, could be smaller than the one corresponding topropagating squeezed Gaussian states.

Similarly, the first experiments on quantum illumina-tion should be performed in an intra-fridge setting. Toour knowledge, no experiments on quantum illumina-tion using microwaves has been realized so far, so weshould aim at performing the first proof-of-principle ex-periments artificially introducing thermal noise and ex-ploring the limits of the quantum signal-to-noise en-hancement. Another interesting proof-of-principle exper-iment would be the use of quantum illumination protocolto detect phase-shift induced cloaking in a highly noisyenvironment [15].

Simultaneously, we must develop single-photon mi-crowave photodetection for flying photons in order toobtain microwave photodetectors with sufficiently highefficiency. A considerable advance in this direction willsubstantially increase the potential success finding real-life and commercial applications of propagating quantummicrowaves. As discussed before, prominent exampleshere are quantum microwave radars or a microwave quan-tum local area network (LAN). We highlight two promis-ing approaches for building an efficient microwave pho-todetector, namely, qubit-based photodetectors [20] andbolometer-based photodetectors [31]. Both show advan-tages and disadvantages, so it would be relevant to followboth approaches in order to determine which one is moreadvantageous at the end for a given problem.

B. Transition from Intra- to Inter-FridgeExperiments

The following natural step is the connection of twodifferent fridges through a millikelvin transmission line.While this may present a challenging engineering task, itis not fundamentally difficult. In contrast, a transmissionline at high temperatures (T = 4−300 K) is a challengingquestion even from a theory point of view, since universalmodels to incorporate losses and decoherence of quantumstates due to the contact with a room-temperature ther-mal bath are not at all tested yet. In any case, we expectthem to be extremely sensitive to the targeted tempera-ture. The losses can be modeled by a beam-splitter cou-

pling the signal to a frequency-dependent thermal bath.If the temperature is not uniform along the waveguide, wecan divide the waveguide into small pieces with constanttemperature and reflectivity and analyze the continuouslimit.

In the field of quantum illumination, a subsequent keyexperiment to determine the feasibility of the researchline in real-life applications consists in a detection prob-lem in which the object and the source of entangledmicrowave radiation are in different fridges, connectedthrough a noisy waveguide. One of the beams remainsin the original fridge, while the other travels through thehighly noisy waveguide, interacts (or not) with a low re-flectivity mirror which models the object and, by detect-ing the reflected signal, one must decide whether the ob-ject is there or not. Also for this scenario, the underlyingtheory work remains to be done.

Finally, quantum microwave technology wouldstrongly profit from engineering filters for thermalphotons, the development of non-reciprocal deviceswhich enhance the efficiency of photodetectors, and thedevelopment of compact delay lines based, for instance,on Josephson metamaterials.

C. Antennae and Open-Air Challenges

The emission and reception of microwave quantum sig-nals by means of antennae is still an open problem, sinceit might require new theoretical and technological devel-opments. Both the theoretical analysis and the type ofantenna are dependent on the type of the signal codifica-tion (in polarization degrees of freedom, or in Fock basis,etc). However, in both cases of low-aperture antennae,such as parabolic or horn antennae, which can focus thesignal in a given direction, seem especially suitable forthese purposes.

The case of entanglement in polarization is somehowsimpler, since there are linearly polarized and circularlypolarized antennae, a feature which is sometimes usedto double the information transmission rate by codify-ing half of the information in one polarization and halfin the other. As the antenna polarization matching isrequired, the information is well preserved. Then, it isnatural to consider the option of sending entangled quan-tum states in polarization degrees of freedom. However,one must take into account that usual technology of su-perconducting circuits inhibits polarization as a degreeof freedom by projecting the electromagnetic field in thewaveguide. There are recently relevant advances in 3Dsuperconducting cavities, which could deal also with po-larization of the microwave photons, but the technologyis by far not as developed as on-chip quasi-1D quantumelectrodynamics yet.

For the purposes related to quantum communication,quantum radar and the implementation of other existingprotocols, entanglement in the number of photons seemsmore suitable. More technically, an antenna can be con-

5

TABLE I. Isotropic path losses LP and absorption losses LA.

Opticsλ= 810 nm,ν= 370 THz

Microwaveλ= 60 mm, ν= 5 GHz

d (km) LP (dB) LA (dB) LP (dB) LA (dB)

' 1 204 3 · 10−2 106 9 · 10−3

' 100 244 3 146 0.9

' 1000 264 30 166 9.0

sidered as an impedance matcher between the supercon-ducting circuit (50 Ohm) and open-air (377 Ohm). Theparadigmatic setup would consist of a quantum source,for instance, a Josephson parametric amplifier (JPA)[32],generating squeezed states, connected by a superconduct-ing waveguide with a 50 Ohm impedance which ends upin the antenna. The antenna smoothly transforms theimpedance of the waveguide into the 377 Ohm impedanceof air. The electromagnetic field propagates throughoutthe space until the receiving antenna takes care of theopposite matching.

Let us briefly analyze communication losses for twotypical examples, one in the optical (λ= 810 nm) and theother in the microwave (λ= 60 mm) regime. To be as gen-eral as possible, we employ the well-known Friis’ formulafor the calculation of the path-losses

L = LAGtGrLP = LAGtGr

(λ

4πd

)2

. (2)

Here, λ is the wavelength of the signal, d the distance,Gt (Gr) the gain of the transmitter (receiver), LA arethe absorption losses, and LP the free-space path lossesfor isotropic antennas. Values for LP and LA are shownfor several characteristic distances in Tab. I. The resultsclearly demonstrate that the pure absorption losses arenegligible in both frequency regimes for d. 100 km as itwould be the case for links to a satellite where absorptionlosses practically vanish above a height of ' 10km. Then,the dominating (isotropic) path losses obviously decreasefor smaller frequencies, which is an encouraging result forthe application of microwaves.

In order to approach a more realistic situation, weshould additionally consider the antenna gains. Assum-ing a perfect parabolic geometry and zero Ohmic losses,the antenna gain can be estimated via the divergenceof the beam it produces. Using this approach, we ob-tain Gt,r = 4π/Ωr,t, where Ωr,t are the solid angles asso-

ciated with the beam divergences θt,r =λ/Dt,r and Dt,r

are the diameters of the transmitter and receiver an-tenna apertures. For our optics example [5], antennagains of 130 dB can be reached for reasonable aperturediameters Dt,r' 1 m. The total loss L is therefore re-duced to approximately 10 dB for parameters similar tothose of the actual satellite quantum communication linkdemonstrated in Ref. [5]. The real losses measured inthat work are higher (' 65 − 82 dB) due to additionalexperimental imperfections not captured by our ideal-ized model. Nevertheless, this experimental attenuationwas small enough to successfully implement quantumkey distribution with sifted key rates of a few kb/s [6].For microwave frequencies, however, the predicted over-all losses are higher. Here, due to the larger wavelength,the decreasing antenna gains outweigh the improvementin isotropic path loss. Increasing the antenna gain via alarger aperture could be useful in quantum illumination(radar) type applications. In quantum communicationscenarios, where large antennas may not be very prac-tical, the parameters from the optics experiment [5, 6]in principle still allow one to cover distances . 100 km.Naturally, the design of heavily optimized microwave an-tennas will be mandatory to reach this challenging goal.For communication distances of a few kilometers, the re-spective requirements are already considerably relaxedand can be viewed as realistic for the near future.

In summary, despite some challenges quantum mi-crowaves propagating in and open air environment ex-hibit a considerable potential for future applications inquantum communication and sensing. To this end, thedevelopment and investigation of suitable antennas andthe development of suitable theory models will be keytasks.

ACKNOWLEDGMENT

The Authors thank M. Mottonen, B. Huard, and Y.Omar for the useful discussions. Authors acknowledgethe EU Flagship project QMiCS. M. S. and E. S. aregrateful for the funding of Spanish MINECO/FEDERFIS2015-69983-P and Basque Government IT986-16.This material is also based upon work supported by theU.S. Department of Energy, Office of Science, Office ofAdvance Scientific Computing Research (ASCR), underfield work proposal number ERKJ335. K. G. F. andF. D. additionally acknowledge financial support fromthe German Research Foundation through FE 1564/1-1, the doctorate program ExQM of the Elite Networkof Bavaria, and the International Max Planck ResearchSchool Quantum Science and Technology.

[1] T. Herbst, T. Scheidl, M. Fink, J. Handsteiner, B.Wittmann, R. Ursin, and A. Zeilinger, “Teleportation of

entanglement over 143 km, Proceedings of the NationalAcademy of Sciences, p. 201517007 (2015).

6

[2] S. Wengerowsky et al., “In-field entanglement distribu-tion over a 96 km-long submarine optical fibre”, arXivpreprint:1803.00583 (2018).

[3] S.-K. Liao et al., “Satellite-to-ground quantum key dis-tribution”, Nature, vol. 549, p. 43 (2017).

[4] J.-G. Ren et al., “Ground-to-satellite quantum telepor-tation”, Nature, vol. 549, p. 70 (2017).

[5] J. Yin et al., “Satellite-based entanglement distributionover 1200 kilometers”, Science, vol. 356, p. 1140 (2017).

[6] S.-K. Liao et al.“Satellite-Relayed IntercontinentalQuantum Network”, Phys. Rev. Lett., vol. 120, p. 030501(2018).

[7] C. L. Degen, F. Reinhard, and P. Cappellaro, “Quantumsensing”, Rev. Mod. Phys., vol. 89, p. 035002 (2017).

[8] E. Oelker, T. Isogai, J. Miller, M. Tse, L. Barsotti,N. Mavalvala, and M. Evans, “Audio-Band Frequency-Dependent Squeezing for Gravitational-Wave Detectors”,Phys. Rev. Lett., vol. 116, p. 041102 (2016).

[9] O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z.Deutsch, and D. Oron, “Superresolution microscopy withquantum emitters”, Nano Lett., vol. 13, p. 5832 (2013).

[10] S. Lloyd, “Enhanced Sensitivity of Photodetection viaQuantum Illumination”, Science, vol. 321, p. 1463 (2008).

[11] E. D. Lopaeva, I. Ruo Berchera, I. P. Degiovanni, S. Oli-vares, G. Brida, and M. Genovese, “Experimental Real-ization of Quantum Illumination”, Phys. Rev. Lett., vol.110, p. 153603 (2013).

[12] G. Brida, M. Genovese, and I. R. Berchera, “Experimen-tal realization of sub-shot-noise quantum imaging”, Nat.Photonics, vol. 4, p. 227 (2010).

[13] T. Nagata, R. Okamoto, J. L. OBrien, K. Sasaki, andS. Takeuchi, “Beating the Standard Quantum Limitwith Four-Entangled Photons”, Science, vol. 316, p. 726(2007).

[14] M. Sanz, and U. Las Heras, J. J. Garcia-Ripoll, E. Solano,and R. Di Candia, “Quantum Estimation Methods forQuantum Illumination”, Phys. Rev. Lett., vol. 118, p.070803 (2017).

[15] U. Las Heras, R. Di Candia, K. G. Fedorov, F. Deppe,M. Sanz, and E. Solano, “Quantum illumination revealsphase-shift inducing cloaking”, Scientific Reports, vol. 7,p. 9333 (2017).

[16] P. Kurpiers et al., “Deterministic Quantum State Trans-fer and Generation of Remote Entanglement using Mi-crowave Photons”, Nature, vol. 558, p. 264 (2018).

[17] R. Di Candia et al., “Quantum teleportation of propa-gating quantum microwaves”, EPJ Quantum Technology,vol. 2, p. 25 (2015).

[18] K. G. Fedorov et al., “Displacement of propagatingsqueezed microwave states”, Phys. Rev. Lett., vol. 117,

p. 020502 (2016).[19] K. G. Fedorov et al., “Finite-time quantum correlations

of propagating squeezed microwaves”, Scientific Reports,vol. 8, p. 6416 (2018).

[20] J.-C. Besse, S. Gasparinetti, M. C. Collodo, T. Walter, P.Kurpiers, M. Pechal, C. Eichler, and A. Wallraff, “Single-Shot Quantum Non-Demolition Detection of ItinerantMicrowave Photons”, Phys. Rev. X, vol. 8, p. 021003(2018).

[21] S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H.Shapiro, and S. Pirandola, “Microwave Quantum Illumi-nation”, Phys. Rev. Lett. vol. 114, p. 080503 (2015).

[22] G. N. Milford, C. C. Harb, and E. H. Huntington, “Shotnoise limited, microwave bandwidth photodetector de-sign”, Rev. Sci. Instrum., vol. 77, no. 11, p. 114701(2006).

[23] G. Romero, J. J. Garcia-Ripoll, and E. Solano, “Pho-todetection of propagating quantum microwaves in cir-cuit QED”, Phys. Scr., vol. T137, p. 014004 (2009).

[24] Y.-F. Chen et al., “Microwave Photon Counter Basedon Josephson Junctions”, Phys. Rev. Lett., vol. 107, p.217401 (2011).

[25] B. Peropadre, G. Romero, G. Johansson, C. M. Wilson,E. Solano, and J. J. Garcıa-Ripoll, “Perfect MicrowavePhotodetection in Circuit QED”, Phys. Rev. A, vol. 84,p. 063834 (2011).

[26] S. R. Sathyamoorthy a, T. M. Stace, and G. Johans-son, “Detecting itinerant single microwave photons”,Comptes Rendus Physique, vol. 17, no. 7, p. 756 (2016).

[27] S. Kono, K. Koshino, Y. Tabuchi, A. Noguchi, and Y.Nakamura, “Quantum non-demolition detection of anitinerant microwave photon”, Nature Physics, vol. 14, p.546 (2018).

[28] J. C. G. Lesurf, “Sky noise”. [Online]. Internet: www.st-andrews.ac.uk/˜www pa/Scots Guide/RadCom/part8/page3.html, 1995 [Accessed: 25- Oct- 2018].

[29] M. Caleffi, “Optimal Routing for Quantum Networks”,IEEE Access, vol. 5, p. 22299 (2017).

[30] M. Caleffi, A. S. Cacciapuoti, and G. Bianchi, “QuantumInternet: from Communication to Distributed Comput-ing!”, NANOCOM18 Proceedings of the 5th ACM Inter-national Conference on Nanoscale Computing and Com-munication (2018).

[31] J. Govenius, R. E. Lake, K. Y. Tan, and M. Mottonen,“Detection of Zeptojoule Microwave Pulses Using Elec-trothermal Feedback in Proximity-Induced JosephsonJunctions”, Phys. Rev. Lett., vol. 117, p. 030802 (2016).

[32] S. Pogorzalek et al., “Hysteretic Flux Response and Non-degenerate Gain of Flux-Driven Josephson ParametricAmplifiers”, Phys. Rev. Applied, vol. 8, p. 024012 (2018).