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Entanglement-assisted Communication System for NASA's Deep-Space Missions:
Feasibility Test and Conceptual Design
Paul Kwiat (U. Illinois, Champaign-Urbana) Hamid Javadi (JPL)
Herb Bernstein (Hampshire College)
Using Quantum Mechanics to defeat Quantum Mechanics
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Outline
1. Motivation: What’s the problem 2. Entanglement: What is it, and how does it help 3. Super-dense Coding: Recent and future data 4. Super-dense Teleportation: Very recent data 5. Other Options
NASA has a critical need for increased data communication rates. We will explore the use of entanglement and hyper-entanglement (simultaneously in multiple photonic degrees of freedom) to achieve efficient code transmission beyond what is possible classically.
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History and Future of Deep Space Communication
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The Problem
Space is BIG.
Space exploration necessarily requires communicating with far away probes.
• need to send instructions to them • need to get data back from them
How to do this efficiently… The Real Problem:
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θ ~ λ/d
QM! The Other Real Problem: Photons obey Uncertainty Principle diffraction beam is very big far away most photons lost
Fraction collected:
QM can help…
d d
E.g., Fmars ~10-6 - 10-7
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Entanglement: What IS it? Entanglement is
“the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought” ––E. Schrödinger
Non-factorizable: cannot be written as a product
|HH⟩ + |VV⟩ = |45,45⟩ + |-45,-45⟩ |HH⟩ - |VV⟩ = |45,-45⟩ + |-45,45⟩ |HV⟩ + |VH⟩ = |45,45⟩ − |-45,-45⟩ |HV⟩ - |VH⟩ = |45,-45⟩ − |-45,45⟩
(like the spin singlet: |↑↓⟩ - |↓↑⟩)
In an entangled state, neither particle has definite properties alone. ⇒ All the information is (nonlocally) stored in the joint properties.
|“0”⟩A|“0”⟩B + |“1”⟩A|“1”⟩B
Example (polarization “Bell states”):
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Two-crystal Polarization-Entangled Source PGK et al. PRA (1999)
A near-perfect ultrabright source of entanglement
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• Polarization (spin)
• Linear momentum
• Orbital angular momentum/spatial mode
• Energy-Time
• Hyper-entangled!
Photon Entanglements
Maximally hyper-entangled state F = 97%; T’s > 94% J. T. Barreiro et al., PRL 95, 260501 (2005)
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Large Hilbert space:
Hyper-entanglement: Particles (photons) simultaneously entangled in multiple DOFs
-More efficient n-qubit transfer: T vs Tn
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Outline
1. Motivation: What’s the problem 2. Entanglement: What is it, and how does it help 3. Super-dense Coding: Recent and future data 4. Super-dense Teleportation 5. Other Options
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“Super-dense coding”
Physical Review Letters
1 photon carries 2 bits of info:
“Super-dents coating”
Bob’s Transformation
I
H ↔ V
V → -V
H ↔ V, V→ -V
Resulting State
HH + VV
HV + VH
HH - VV
HV - VH
Source of entangled photons: HH + VV
BOB encoder
ALICE Bell-state analysis
1 photon
1 photon
2 bits 2 bits
1 photon
Channel cap. = log24 = 2 bits/photon
Entanglement: Why does/might it help?
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1:
2:
Kwiat & Weinfurter, PRA 58, R2623 (1998)
Quantum SuperDense Coding
CNOT interferometer
Polarization Bell states:
1
Spatial mode Ancillary DOF
Walborn et al., PRA 68, 042313 (2003)
<Psuccess>= 95%
Implement high-capacity quantum superdense coding: Barreiro, Wei, PGK, Nat. Phys. 4, 282 (2008)
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Super- and Hyper-dense Coding “Classically”: only 1 bit can be transferred/ photon*
⇒ This is one of our main experimental goals for the rest of Phase I
Super-dense Coding: up to 2 bits/photon Our group: 1.63 bit/photon (world record)
Hyper-dense Coding – Use simultaneous entanglement in multiple DOFs: E.g., Bob can send one of 16 states. Alice can decode up to 7: up to 2.8 bits/photon
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Spacecraft Memory
Sym
bo
l 2
Sym
bo
l 3
2. Each half of ~106 entangled photon pairs is coded with the same message
2’. Hyper-entanglement encodes multiple bits (e.g., 4) via multiple DOFs
Entangled pair
4. Joint measurement made on received photon and entangled companion
Deep-Space Quantum Communication How does it work?
1. Assume that (hyper)entanglement is pre-shared between space-craft and transmitter.
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Outline
1. Motivation: What’s the problem 2. Entanglement: What is it, and how does it help 3. Super-dense Coding: Recent and future data 4. Super-dense Teleportation 5. Other Options
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Hyper-entanglement-enhanced quantum communication (“Super-dense Teleportation”) A full communication ‘portfolio’ should include transmission of quantum information:
Binary digit -- “bit” 0, 1
copyable
Quantum bit -- “qubit” |0⟩, |1⟩, (|0⟩ + |1⟩)/√2
unclonable
Because of superpositions, the qubit has an infinite amount more information (2 continuous parameters*):
|ψ⟩ = cosθ |0⟩ + eiφ sinθ |1⟩ * like latitude and longitude
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|?⟩ = |“Kirk”⟩
|“Kirk”⟩
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|?⟩ = |“Kirk”⟩
|“Kirk”⟩
Bennett et al., PRL 70, 1895 (1993)
Bell state
analysis
Unitary Transform
|ψ−⟩ = |HV⟩ − |VH⟩
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“Super-dense Teleportation” By using a restricted set of quantum states, it’s possible to transfer as many parameters, with fewer classical resources. |ψ⟩ = |0⟩ + eiα |1⟩ + eiβ |2⟩ +…
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Super-dense Teleportation Remotely prepare |ψ⟩ = |0⟩ + eiα|1⟩ + eiβ |2⟩ + eiγ |3⟩
Fidelity 82%
Re ψ Im ψ Send α = 270° β = 346 γ = 0°
First data (5am, 3/28/2012)
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Kwiat’s Quantum Clan (2012) Graduate Students: Kevin McCusker Aditya Sharma Kevin Zielnicki Trent Graham Brad Christensen Rebecca Holmes
Undergraduates: Daniel Kumor David Schmid Mae Teo Jia Jun (“JJ”) Wong Ben Chng Zhaoqi Leng Joseph Nash Cory Alford Brian Huang
Post-Doc: Jian Wang
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Outline
1. Motivation: What’s the problem 2. Entanglement: What is it, and how does it help 3. Super-dense Coding: Recent and future data 4. Super-dense Teleportation 5. Other Options
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H
R
V
L
Other Potential Methods to Improve Classical Channel Capacity
-Multi-photon Optimal Quantum State Discrimination
If you have only one qubit, then only 2 quantum states (= 1 bit) may be reliable distinguished:
With multiple copies, one may be able to discriminate more states (“messages”) efficiently (especially with adaptive techniques):
E.g., 8 states 3 bits
-Quantum Super-additivity (“2 heads are better than 2!”)
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Summary 1. Motivation: NASA has a critical need for increased data rates.
2. Entanglement: Nonlocal quantum correlations in one/more DOFs
3. Super-dense Coding: Nonlocal quantum correlations in one/more DOFs
4. Super-dense Teleportation: Remotely prepare quantum state with reduced classical communication. First DATA!
5. Other Options: Adaptive, multi-photon state discrimination, …
We will explore the use of entanglement and hyper-entanglement (simultaneously in multiple photonic degrees of freedom) to achieve efficient code transmission beyond what is possible classically.
How far can we go?
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* Not intended to represent our proposed timeline, budget or required resources.
“To infinity… and beyond.*”
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NASA’s vision for construction of planetary and interplanetary networks
from Charles B Shah [email protected]
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Spacecraft Memory
Sym
bo
l 2
Sym
bo
l 3
2. Each half of ~106 entangled photon pairs is coded with the same message (symbols 1-4)
2’. A hyper-entangled single photon carries additional information in its multiple DOFs, e.g., 4 bits
Entangled pair
4. Joint measurement made on received photon and entangled companion
Deep-Space Quantum Communication How does it work?
1. Assume that (hyper)entanglement is pre-shared between space-craft and transmitter.
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Memory
Sym
bo
l 2
Sym
bo
l 3
Zillions* of entangled photon pairs in a
symbol are coded with the
same message
A hyper-entangled single photon
carries additional information
in its multiple degrees of freedoms.
Entangled pair =
Companion of the detected photon pops out of the ensemble
stored in the memory
Deep-Space Quantum Communication How does it work?
* actually, more like 107
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Experimentally reported CC for quantum dense coding
Pol.-Time hyperentangl. Schuck et al. (2006) Polarization
Mattle et al. (1996)
Ions (2004) Schaetz et al.
Limit for classical dense coding, CC=1bit
Limit for standard quantum dense coding with linear optics, CC=1.585 bits
Spin-Orbit hyperent. CC=1.630(6)
CC = 2.81 bits*
*Wei / Barreiro / Kwiat, PRA (2007) Barreiro, Wei, PGK, Nat. Phys. 4, 282 (2008)
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Two-crystal Polarization-Entangled Source
Tune pump polarization: Nonmax. entangled states PRL 83, 3103 (1999)
Spatial-compensation: all pairs have same phase φ OptExp.13, 8951 (2005
PGK et al. PRA (1999)
Temporal pre-compensation: works with fs-laser OptExp.17, 18920 (2009)
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|H⟩|H⟩ + |V⟩|V⟩ = |45⟩|45⟩ + |-45⟩|-45⟩
• Near-perfect quantum behavior • Ultrabright source
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Why hyperentanglement helps… an intuitive view:
Hyperentanglement allows access to enlarged Hilbert space
Without hyperentanglement: With hyperentanglement:
Can only reliably distinguish
these
Can reliably distinguish all four
polarization Bell states
These two give the same
experimental signature
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1:
2:
Kwiat & Weinfurter, PRA 58, R2623 (1998)
Bell-state analysis
CNOT interferometer
Polarization Bell states:
1
Spatial mode Ancillary DOF
Walborn et al., PRA 68, 042313 (2003)
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Outline
1. Entangled/Hyper-entangled State Preparation 2. Bell State Analysis 3. Direct Characterization of Quantum Dynamics 4. Hyper-entangled QKD
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Entanglement: Why does/might it help? Entanglement is
“the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought” ––E. Schrödinger
Non-factorizable: cannot be written as a product ⇒ Entanglement Example (“Bell states”): |HH⟩ + |VV⟩ = |45,45⟩ + |-45,-45⟩ |HH⟩ - |VV⟩ = |45,-45⟩ + |-45,45⟩ |HV⟩ + |VH⟩ = |45,45⟩ − |-45,-45⟩ |HV⟩ - |VH⟩ = |45,-45⟩ − |-45,45⟩
(like the spin singlet: |↑↓⟩ - |↓↑⟩)
In an entangled state, neither particle has definite properties alone. ⇒All the information is (nonlocally) stored in the joint properties.
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• Quantum processes may be represented by a χ matrix:
• Multiple quantum state tomographies are required to characterize ε. • A general n-qubit process tomography requires 16n measurements,
e.g., 1-qubit process: full state tomography (4 measurements each) for each of 4 input states.
Review of Standard Quantum Process Tomography (SQPT)
3†
, 0
( ) mn m nm n
ε ρ χ σ ρσ=
= ∑
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Direct Characterization of Quantum Dynamics (DCQD)*
* M. Mohseni and D. A. Lidar, Phys. Rev. Lett. 97, 170501 (2006)
• It is possible to use a larger Hilbert space to decrease the number of required measurements. Only 4n required.
• DCQD uses entangled states to characterize processes.
• No tomography, only 2-qubit gates (e.g., Bell state analysis)** [other reduced-measurement schemes require n-qubit interactions].
** Z.-W. Wang et al., PRA 75, 044304 (2007); W.-T. Liu et al., PRA 77, 032328 (2008)
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Polarization-entangled pairs generated by two-crystal source
Spontaneous Parametric Down Conversion Type-I phase matching
Conservation of energy Energy entanglement
Conservation of momentum Linear momentum entanglement & orbital angular momentum entanglement
Ç(2)
Pump Laser
Maximal polarization
entanglement
(2)
Tune pump polarization: nonmax. entangled states PRL 83, 3103 (1999)
Spatial-compensation: all pairs have same phase φ OptExp.13, 8951 (2005
Temporal pre-compensation: works with fs-laser OptExp.17, 18920 (2009)
(and BiBO)
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Outline
1. Entangled/Hyper-entangled State Preparation 2. Bell State Analysis 3. Direct Characterization of Quantum Dynamics 4. Hyper-entangled QKD