# Demonstration of entanglement-by-measurement of solid-state qubits

## Abstract

Projective measurements are a powerful tool for manipulating quantum states1,2,3,4,5,6,7,8,9,10,11,12,13. In particular, a set of qubits can be entangled by measuring a joint property3,4,5,6,7,8,9,10,11,12,13 such as qubit parity. These joint measurements do not require a direct interaction between qubits and therefore provide a unique resource for quantum information processing with well-isolated qubits. Numerous schemes for entanglement-by-measurement of solid-state qubits have been proposed8,9,10,11,12,13, but the demanding experimental requirements have so far hindered implementations. Here we realize a two-qubit parity measurement on nuclear spins localized near a nitrogen-vacancy centre in diamond by exploiting an electron spin as a readout ancilla. The measurement enables us to project the initially uncorrelated nuclear spins into maximally entangled states. By combining this entanglement with single-shot readout we demonstrate the first violation of Bell’s inequality with solid-state spins. These results introduce a new class of experiments in which projective measurements create, protect and manipulate entanglement between solid-state qubits.

## Access options

from\$8.99

All prices are NET prices.

## References

1. 1

Raussendorf, R. & Briegel, H. J. A one-way quantum computer. Phys. Rev. Lett. 86, 5188–5191 (2001).

2. 2

Kok, P. et al. Linear optical quantum computing with photonic qubits. Rev. Mod. Phys. 79, 135–174 (2007).

3. 3

Cabrillo, C., Cirac, J., Garcia-Fernandez, P. & Zoller, P. Creation of entangled states of distant atoms by interference. Phys. Rev. A 59, 1025–1033 (1999).

4. 4

Bose, S., Knight, P., Plenio, M. & Vedral, V. Proposal for teleportation of an atomic state via cavity decay. Phys. Rev. Lett. 83, 5158–5161 (1999).

5. 5

Chou, C. W. et al. Measurement-induced entanglement for excitation stored in remote atomic ensembles. Nature 438, 828–832 (2005).

6. 6

Riebe, M. et al. Deterministic entanglement swapping with an ion-trap quantum computer. Nature Phys. 4, 839–842 (2008).

7. 7

Olmschenk, S. et al. Quantum teleportation between distant matter qubits. Science 323, 486–489 (2009).

8. 8

Beenakker, C. W. J., DiVincenzo, D. P., Emary, C. & Kindermann, M. Charge detection enables free-electron quantum computation. Phys. Rev. Lett. 93, 020501 (2004).

9. 9

Mao, W., Averin, D. V., Ruskov, R. & Korotkov, A. N. Mesoscopic quadratic quantum measurements. Phys. Rev. Lett. 93, 056803 (2004).

10. 10

Engel, H-A. & Loss, D. Fermionic Bell-state analyzer for spin qubits. Science 309, 586–588 (2005).

11. 11

Trauzettel, B., Jordan, A. N., Beenakker, C. W. J. & Büttiker, M. Parity meter for charge qubits: An efficient quantum entangler. Phys. Rev. B 73, 235331 (2006).

12. 12

Lalumière, K., Gambetta, J. M. & Blais, A. Tunable joint measurements in the dispersive regime of cavity QED. Phys. Rev. A 81, 040301 (2010).

13. 13

Ionicioiu, R. Entangling spins by measuring charge: A parity-gate toolbox. Phys. Rev. A 75, 032339 (2007).

14. 14

Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, 2001).

15. 15

Dutt, M. V. G. et al. Quantum register based on individual electronic and nuclear spin qubits in diamond. Science 316, 1312–1316 (2007).

16. 16

Neumann, P. et al. Multipartite entanglement among single spins in diamond. Science 320, 1326–1329 (2008).

17. 17

Neumann, P. et al. Single-shot readout of a single nuclear spin. Science 329, 542–544 (2010).

18. 18

Fuchs, G. D., Burkard, G., Klimov, P. V. & Awschalom, D. D. A quantum memory intrinsic to single nitrogen-vacancy centres in diamond. Nature Phys. 7, 789–793 (2011).

19. 19

Waldherr, G., Neumann, P., Huelga, S. F., Jelezko, F. & Wrachtrup, J. Violation of a temporal Bell inequality for single spins in a diamond defect center. Phys. Rev. Lett. 107, 090401 (2011).

20. 20

Robledo, L. et al. High-fidelity projective read-out of a solid-state spin quantum register. Nature 477, 574–578 (2011).

21. 21

Jiang, L. et al. Coherence of an optically illuminated single nuclear spin qubit. Phys. Rev. Lett. 100, 073001 (2008).

22. 22

Aharonovich, I., Greentree, A. D. & Prawer, S. Diamond photonics. Nature Photon. 5, 397–405 (2011).

23. 23

Batalov, A. et al. Low temperature studies of the excited-state structure of negatively charged nitrogen-vacancy color centers in diamond. Phys. Rev. Lett. 102, 195506 (2009).

24. 24

Ansmann, M. et al. Violation of Bell’s inequality in Josephson phase qubits. Nature 461, 504–506 (2009).

25. 25

Rowe, M. A. et al. Experimental violation of a Bell’s inequality with efficient detection. Nature 409, 791–794 (2001).

26. 26

Ladd, T. D. et al. Quantum computers. Nature 464, 45–53 (2010).

27. 27

Morello, A. et al. Single-shot readout of an electron spin in silicon. Nature 467, 687–691 (2010).

28. 28

Morton, J. J. L. et al. Solid-state quantum memory using the 31P nuclear spin. Nature 455, 1085–1088 (2008).

29. 29

Togan, E. et al. Quantum entanglement between an optical photon and a solid-state spin qubit. Nature 466, 730–734 (2010).

30. 30

Bernien, H. et al. Two-photon quantum interference from separate nitrogen vacancy centers in diamond. Phys. Rev. Lett. 108, 043604 (2012).

31. 31

Sipahigil, A. et al. Quantum interference of single photons from remote nitrogen-vacancy centers in diamond. Phys. Rev. Lett. 108, 143601 (2012).

## Acknowledgements

We thank D. D. Awschalom, L. Childress, L. DiCarlo, V. V. Dobrovitski, G. D. Fuchs and J. J. L. Morton for helpful discussions and comments, and R. N. Schouten for technical assistance. We acknowledge support from the Dutch Organization for Fundamental Research on Matter (FOM), the Netherlands Organization for Scientific Research (NWO), the DARPA QuEST and QuASAR programmes, and the EU SOLID and DIAMANT programmes.

## Author information

W.P., T.H.T. and L.R. carried out the experiment. W.P. and T.H.T. analysed the data. H.B. fabricated the sample. M.M. and D.J.T. grew the diamond. W.P., T.H.T. and R.H. wrote the manuscript. All authors commented on the manuscript. R.H. supervised the project.

Correspondence to Ronald Hanson.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Supplementary information

### Supplementary Information

Supplementary Information (PDF 2030 kb)

## Rights and permissions

Reprints and Permissions

Pfaff, W., Taminiau, T., Robledo, L. et al. Demonstration of entanglement-by-measurement of solid-state qubits. Nature Phys 9, 29–33 (2013) doi:10.1038/nphys2444

• #### DOI

https://doi.org/10.1038/nphys2444

• ### Error correction of quantum system dynamics via measurement–feedback control

• Du Ran
• , Zhi-Cheng Shi
• , Zhen-Biao Yang
• , Jie Song
•  & Yan Xia

Journal of Physics B: Atomic, Molecular and Optical Physics (2019)

• ### Dynamically Polarizing Spin Register of N- V Centers in Diamond Using Chopped Laser Pulses

• Nanyang Xu
• , Yu Tian
• , Bing Chen
• , Jianpei Geng
• , Xiaoxiong He
• , Ya Wang
•  & Jiangfeng Du

Physical Review Applied (2019)

• ### Multipartite Entanglement Generation and Contextuality Tests Using Nondestructive Three-Qubit Parity Measurements

• S. B. van Dam
• , J. Cramer
• , T. H. Taminiau
•  & R. Hanson

Physical Review Letters (2019)

• ### Floquet engineering to entanglement protection of distant nitrogen vacancy centers

• W L Yang
• , W L Song
• , Jun-Hong An
• , M Feng
• , D Suter
•  & Jiangfeng Du

New Journal of Physics (2019)