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