demonstration of entanglement-by-measurement in solid-state … · 2017. 6. 21. · references...
TRANSCRIPT
Demonstration of
entanglement-by-measurement
in solid-state qubits
Presented by: Ernest Tan
▪ Physical system
▪ Performing measurements
▪ Ancilla readout
▪ Two-qubit measurements
▪ Generating entanglement
▪ Initialisation
▪ Entanglement-by-measurement
▪ Verifying entanglement
▪ State tomography
▪ Bell violation
Outline
▪ Nitrogen (N) next to vacancy (V) in diamond lattice
▪ N-V0 and N-V– charge states
▪ Green light (532nm) to generate/restore N-V–
▪ Use three quantum systems in N-V–
▪ Electron pair (triplet state, spin-1)
▪ Nitrogen-14 nucleus (spin-1)
▪ Carbon-13 nucleus (spin-½)
Nitrogen vacancies
Entangled qubits
Ancilla
Energy levels
Energy levels
▪ Preparation
▪ Long (200μs) Ex pulse
▪ Pumps into mS = ±1 via coupling
▪ Single-shot readout
▪ Short (10μs) Ex pulse
▪ Always interpreted as 0/1 outcome
▪ Non-destructive readout
▪ Very short (200ns) Ex pulse
▪ Interpreted as 0/abort (~94% probability abort)
Ancilla electron
▪ Initialised in mS = 0:
▪ Average 6.4 photons emitted
▪ Some probability of no emission
▪ Initialised in mS = ±1:
▪ Almost always no photons emitted
▪ Therefore:
▪ Photons > threshold ⇒ mS = 0 (very likely)
▪ Photons < threshold ⇒ mS = ±1 (some uncertainty)
Ancilla electron readout
Nuclear qubits
▪ 4-outcome measurement
Nuclear qubit measurement (computational basis)
Permute, take average
Nuclear qubit measurement (arbitrary separable basis)
Initialisation of ȁ𝟎𝟎 state
ȁ1 ȁ00 + ȁ01 + ȁ10 + ȁ11
ȁ0 ȁ00 + ȁ11 + ȁ1 ȁ01 + ȁ10
ȁ0 ȁ00 + ȁ11
Entanglement by measurement
(normalisation factors omitted)
ȁ100
Couple to
ancilla
Measure ancilla,
postselect
Single-qubit
rotations
= ȁ0 + ȁ1 ȁ0 + ȁ1(still a separable state)
Entanglement by measurement
Experiment flow
Implements arbitrary
(separable) measurementGenerates entangled state
State tomography
𝜌 =1
4𝐼⨂𝐼 + Ԧ𝑎 ∙ Ԧ𝜎 ⨂𝐼 + 𝐼⨂ 𝑏 ∙ Ԧ𝜎 +
𝑗,𝑘
𝑡𝑗𝑘𝜎𝑗⨂𝜎𝑘
𝜎𝑗 ⊗ 𝐼 = 𝑎𝑗 𝐼 ⊗ 𝜎𝑗 = 𝑏𝑗 𝜎𝑗 ⊗𝜎𝑘 = 𝑡𝑗𝑘
▪ Fidelity of prepared computational-basis state: ~96%
▪ Accounted for by limited ancilla reset (only returns ~96% of electron population to mS = –1 )
▪ Fidelity of final entangled state: < 92%
▪ Because ancilla reset occurs twice
Fidelities and losses
Other Bell states (preparation and verification)
Bell tests: the CHSH game
𝐴 𝐵
𝑏𝑎 𝐴, 𝐵, 𝑎, 𝑏 = ±1
𝐴𝐵 + 𝐴𝑏 + 𝑎𝐵 + −𝑎𝑏
𝐴𝐵 + 𝐴𝑏 + 𝑎𝐵 + −𝑎𝑏
= 𝐴𝐵 + 𝐴𝑏 + 𝑎𝐵 − 𝑎𝑏
= 𝐴(𝐵 + 𝑏) + 𝑎(𝐵 − 𝑏)
=
≤ 2
The CHSH inequality
something that’s always ±2
▪ (Ideal) QM value: 𝐴𝐵 + 𝐴𝑏 + 𝑎𝐵 + −𝑎𝑏 = 2 2 > 2 !
▪ Pre-existing values?
▪ Pre-existing “instructions”?
The CHSH inequality
Impossible!
Must be “nonlocal”!
“Nonlocality”
▪ CHSH inequality: 𝐶1𝑁1 − 𝐶1𝑁2 − 𝐶2𝑁1 − 𝐶2𝑁2 ≤ 2▪ Value >2 indicates entanglement
Bell violation
= 𝑃 00 + 𝑃 11 − 𝑃 01 − 𝑃(10)
Modification for Bell test (avoid fair-sampling loophole)
▪ Photons coupled to NV-centre electrons
Extension: loophole-free Bell test
▪ Generate entanglement by measurement
▪ Entangled state verified with high fidelity
▪ Bell violation observed
Summary
References
▪ Pfaff, W. et al. Demonstration of entanglement-by-measurement of solid-state
qubits. Nat Phys 9, 29–33 (2013).
▪ Robledo, L. et al. High-fidelity projective read-out of a solid-state spin quantum
register. Nature 477, 574–578 (2011).
▪ Hensen, B. et al. Loophole-free Bell inequality violation using electron spins
separated by 1.3 kilometres. Nature 526, 682–686 (2015).
▪ Neumann, P. et al. Multipartite Entanglement Among Single Spins in Diamond.
Science 320, 1326–1329 (2008).
▪ Doherty, M. W. et al. The nitrogen-vacancy colour centre in diamond. Physics
Reports 528, 1–45 (2013).
Images from:
▪ http://www.uni-saarland.de/fak7/becher/News/news_engl.html