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Quantum Information Processing

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01-05-2021

Violation of Bell’s inequalities by continuous probing of a two-qubit system

Authors: Peng Xu, Peng Zhao, Wei Zhong, Shengmei Zhao

Published in: Quantum Information Processing | Issue 5/2021

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Abstract

We theoretically analyze the Bell’s inequalities by continuously monitoring a system comprising two-coupled superconducting qubits. The weak probing could measure the observables accurately after sufficient runs. While for the strong measurement, due to the measurement backaction, the system will collapse to the basis state corresponding to the eigenvalue measured with a higher probability. Interestingly, for system in the maximal two-qubit entanglement state, the measurement backaction from strong probe could be compensated by a parity measurement. Under the imperfect detection, a correction term could help yield a result which is compatible with the correct value of the observables. Furthermore, we investigate the Bell’s inequalities during the dynamical evolution of the coupled two-qubit system and demonstrate that the more the two-qubit entangle, the larger violation of Bell’s inequality will present with the upper bound \(2\sqrt{2}\).

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Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)ADSCrossRef

Bell, J.-S.: On the einstein podolsky rosen paradox. Physics 1, 195 (1964)MathSciNetCrossRef

Yu, S., Chen, Z.-B., Pan, J.-W., Zhang, Y.-D.: Classifying N-qubit entanglement via Bell’s inequalities. Phys. Rev. Lett. 90, 080401 (2003)ADSMathSciNetCrossRef

Clauser, J.-F., Horne, M.-A., Shimony, A., Holt, R.-A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880 (1969)ADSCrossRef

Aspect, A., Grangier, P., Roger, G.: Experimental realization of Einstein-Podolsky-Rosen-Bohm gedankenexperiment: a new violation of Bell’s inequalities. Phys. Rev. Lett. 49, 91 (1982)ADSCrossRef

Kuzmich, A., Walmsley, I.-A., Mandel, L.: Violation of Bell’s inequality by a generalized Einstein-Podolsky-Rosen state using homodyne detection. Phys. Rev. Lett. 85, 1349 (2000)ADSMathSciNetCrossRef

Ruskov, R., Korotkov, A.-N., Mizel, A.: Signatures of quantum behavior in single-qubit weak measurements. Phys. Rev. Lett. 96, 200404 (2006)ADSCrossRef

Chen, Z.-B., Pan, J.-W., Hou, G., Zhang, Y.-D.: Maximal violation of Bell’s inequalities for continuous variable systems. Phys. Rev. Lett. 88, 040406 (2002)ADSCrossRef

Blais, A., Huang, R.-S., Wallraff, A., Girvin, S.-M., Schoelkopf, R.-J.: Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation. Phys. Rev. A 69, 062320 (2004)ADSCrossRef

10.

Blais, A., Gambetta, J., Wallraff, A., Schuster, D.-I., Girvin, S.-M., Devoret, M.-H., Schoelkopf, R.-J.: Quantum-information processing with circuit quantum electrodynamics. Phys. Rev. A 75, 032329 (2007)ADSCrossRef

11.

Koch, J., Yu, T.-M., Gambetta, J., Houck, A.-A., Schuster, D.-I., Majer, J., Blais, A., Devoret, M.-H., Girvin, S.-M., Schoelkopf, R.-J.: Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007)ADSCrossRef

12.

Xiang, Z.-L., Ashhab, S., You, J.-Q., Nori, F.: Hybrid quantum circuits: superconducting circuits interacting with other quantum systems. Rev. Mod. Phys. 85, 623 (2013)ADSCrossRef

13.

Ansmann, M., Wang, H., Bialczak, R.-C., Hofheinz, M., Lucero, E., Neeley, M., O’Connell, A.-D., Sank, D., Weides, M., Wenner, J., Cleland, A.-N., Martinis, J.-M.: Violation of Bell’s inequality in Josephson phase qubits. Nature 461, 504 (2009)ADSCrossRef

14.

Palacios-Laloy, A., Mallet, F., Nguyen, F., Bertet, P., Vion, D., Esteve, D., Korotkov, A.-N.: Experimental violation of a Bell’s inequality in time with weak measurement. Nat. Phys. 6, 442 (2010)CrossRef

15.

Zhong, Y.-P., Chang, H.-S., Satzinger, K.J., Chou, M.-H., Bienfait, A., Conner, C.-R., Dumur, É., Grebel, J., Peairs, G.-A., Povey, R.-G., Schuster, D.-I., Cleland, A.-N.: Violating Bell’s inequality with remotely connected superconducting qubits. Nat. Phys. 15, 741–744 (2019)CrossRef

16.

Ma, Y., Pan, X., Cai, W., Mu, X., Xu, Y., Hu, Y., Wang, W., Wang, H., Song, Y.-P., Yang, Z.-B., Zheng, S.-B., Sun, L.: Manipulating complex hybrid entanglement and testing multipartite Bell inequalities in a superconducting circuit. Phys. Rev. Lett. 125, 180503 (2020)ADSCrossRef

17.

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

18.

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

19.

Nielsen, M.-A., Chuang, I.-L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)MATH

20.

Ahn, C., Doherty, A.-C., Landahl, A.-J.: Continuous quantum error correction via quantum feedback control. Phys. Rev. A 65, 042301 (2002)ADSCrossRef

21.

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)ADSCrossRef

22.

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

23.

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

24.

Pfaff, W., Taminiau, T.-H., Robledo, L., Bernien, H., Markham, M., Twitchen, D.-J., Hanson, R.: Demonstration of entanglement-by-measurement of solid-state qubits. Nat. Phys. 9, 29 (2013)CrossRef

25.

Ristè, D., Dukalski, M., Watson, C.-A., de Lange, G., Tiggelman, M.-J., Blanter, Y.-M., Lehnert, K.-W., Schouten, R.-N., Dicarlo, L.: Deterministic entanglement of superconducting qubits by parity measurement and feedback. Nature 502, 350 (2013)ADSCrossRef

26.

Wootters, W.-K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)ADSCrossRef

27.

Wootters, W.-K.: Entanglement of formation and concurrence. Quant. Inf. and Comp. 1, 27 (2001)MathSciNetMATH

28.

Kar, G.: Noncommuting spin-1 2 observables and the CHSH inequality. Phys. Lett. A. 204, 99 (1995)ADSMathSciNetCrossRef

29.

Majer, J., Chow, J.-M., Gambetta, J.-M., Koch, J., Johnson, B.-R., Schreier, J.-A., Frunzio, L., Schuster, D.-I., Houck, A.-A., Wallraff, A., Blais, A., Devoret, M.-H., Girvin, S.-M., Schoelkopf, R.-J.: Coupling superconducting qubits via a cavity bus. Nature 449, 443 (2007)ADSCrossRef

30.

Hatridge, M., Shankar, S., Mirrahimi, M., Schackert, F., Geerlings, K., Brecht, T., Sliwa, K.-M., Abdo, B., Frunzio, L., Girvin, S.-M., Schoelkopf, R.-J., Devoret, M.-H.: Quantum back-action of an individual variable-strength measurement. Science 339, 178 (2013)ADSMathSciNetCrossRef

31.

Weber, S.-J., Chantasri, A., Dressel, J., Jordan, A.-N., Murch, K.-W., Siddiqi, I.: Mapping the optimal route between two quantum states. Nature 511, 570 (2014)ADSCrossRef

32.

Jacobs, K.: Stochastic Processes for Physicists: Understanding Noisy Systems. Cambridge University Press, Cambridge, UK (2010)CrossRef

33.

Wiseman, H.-M., Milburn, G.-J.: Quantum Measurement and Control. Cambridge University Press, Cambridge, UK (2010)MATH

34.

Xu, P., Kiilerich, A.-H., Blattmann, R., Yu, Y., Zhu, S.-L., Møllmer, K.: Measurement of the topological Chern number by continuous probing of a qubit subject to a slowly varying Hamiltonian. Phys. Rev. A 96, 010101(R) (2017)ADSMathSciNetCrossRef

Title: Violation of Bell’s inequalities by continuous probing of a two-qubit system
Authors: Peng Xu
Peng Zhao
Wei Zhong
Shengmei Zhao
Publication date: 01-05-2021
Publisher: Springer US
Published in: Quantum Information Processing / Issue 5/2021
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI: https://doi.org/10.1007/s11128-021-03085-1

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