Separation of quantum, spatial quantum, and approximate quantum correlations
QuOne Lab, Phanous Research and Innovation Centre, Tehran, Iran
Published: | 2021-01-28, volume 5, page 389 |
Eprint: | arXiv:2004.11103v2 |
Doi: | https://doi.org/10.22331/q-2021-01-28-389 |
Citation: | Quantum 5, 389 (2021). |
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Abstract
Quantum nonlocal correlations are generated by implementation of local quantum measurements on spatially separated quantum subsystems. Depending on the underlying mathematical model, various notions of sets of quantum correlations can be defined. In this paper we prove separations of such sets of quantum correlations. In particular, we show that the set of bipartite quantum correlations with four binary measurements per party becomes strictly smaller once we restrict the local Hilbert spaces to be finite dimensional, $\textit{i.e.}$, $\mathcal{C}_{\text{$\rm{q}$}}^{(4, 4, 2,2)} \neq \mathcal{C}_{\text{$\rm{qs}$}}^{(4, 4, 2,2)}$. We also prove non-closure of the set of bipartite quantum correlations with four ternary measurements per party, $\textit{i.e.}$, $\mathcal{C}_{\text{$\rm{qs}$}}^{(4, 4, 3,3)} \neq \mathcal{C}_{\text{$\rm{qa}$}}^{(4, 4, 3,3)}$.
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[1] A. Acín, S. Massar, and S. Pironio. Randomness versus nonlocality and entanglement. Physical Review Letters, 108 (10): 100402, 2012. 10.1103/PhysRevLett.108.100402.
https://doi.org/10.1103/PhysRevLett.108.100402
[2] C. Bamps and S. Pironio. Sum-of-squares decompositions for a family of CHSH-like inequalities and their application to self-testing. Physical Review A, 91 (5): 052111, 2015. 10.1103/PhysRevA.91.052111.
https://doi.org/10.1103/PhysRevA.91.052111
[3] J. S. Bell. On the Einstein Podolsky Rosen paradox. Physics, 1: 195, 1964. 10.1103/PhysicsPhysiqueFizika.1.195.
https://doi.org/10.1103/PhysicsPhysiqueFizika.1.195
[4] J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt. Proposed experiment to test local hidden-variable theories. Physical Review Letters, 23 (15): 880, 1969. 10.1103/PhysRevLett.23.880.
https://doi.org/10.1103/PhysRevLett.23.880
[5] A. Coladangelo. Generalization of the Clauser-Horne-Shimony-Holt inequality self-testing maximally entangled states of any local dimension. Physical Review A, 98 (5): 052115, 2018. 10.1103/PhysRevA.98.052115.
https://doi.org/10.1103/PhysRevA.98.052115
[6] A. Coladangelo. A two-player dimension witness based on embezzlement, and an elementary proof of the non-closure of the set of quantum correlations. Quantum, 4: 282, 2020. 10.22331/q-2020-06-18-282.
https://doi.org/10.22331/q-2020-06-18-282
[7] A. Coladangelo and J. Stark. Unconditional separation of finite and infinite-dimensional quantum correlations. arXiv:1804.05116 [quant-ph], 2018.
arXiv:1804.05116
[8] A. Coladangelo, K. T. Goh, and V. Scarani. All pure bipartite entangled states can be self-tested. Nature Communications, 8: 15485, 2017. 10.1038/ncomms15485.
https://doi.org/10.1038/ncomms15485
[9] K. Dykema, V. I. Paulsen, and J. Prakash. Non-closure of the set of quantum correlations via graphs. Communications in Mathematical Physics, 365: 1125–1142, 2019. 10.1007/s00220-019-03301-1.
https://doi.org/10.1007/s00220-019-03301-1
[10] A. Einstein, B. Podolsky, and N. Rosen. Can quantum-mechanical description of physical reality be considered complete? Physical Review, 47: 777, 1935. 10.1103/PhysRev.47.777.
https://doi.org/10.1103/PhysRev.47.777
[11] T. Fritz. Tsirelson's problem and Kirchberg's conjecture. Reviews in Mathematical Physics, 24 (5): 1250012, 2012. 10.1142/S0129055X12500122.
https://doi.org/10.1142/S0129055X12500122
[12] Z. Ji, A. Natarajan, T. Vidick, J. Wright, and H. Yuen. $\text{MIP}^\ast=\text{RE}$. arXiv:2001.04383 [quant-ph], 2020.
arXiv:2001.04383
[13] D. Leung, B. Toner, and J. Watrous. Coherent state exchange in multi-prover quantum interactive proof systems. Chicago Journal of Theoretical Computer Science, pages 1–18, 2013. 10.4086/cjtcs.2013.011.
https://doi.org/10.4086/cjtcs.2013.011
[14] M. Musat and M. Rørdam. Non-closure of quantum correlation matrices and factorizable channels that require infinite dimensional ancilla. Communications in Mathematical Physics, 2019. 10.1007/s00220-019-03449-w.
https://doi.org/10.1007/s00220-019-03449-w
[15] K. F. Pál and T. Vértesi. Maximal violation of the I3322 inequality using infinite dimensional quantum systems. Physical Review A, 82 (2): 022116, 2010. 10.1103/PhysRevA.82.022116.
https://doi.org/10.1103/PhysRevA.82.022116
[16] A. Salavrakos, R. Augusiak, J. Tura, P. Wittek, A. Acín, and S. Pironio. Bell inequalities tailored to maximally entangled states. Physical Review Letters, 119: 040402, 2017. 10.1103/PhysRevLett.119.040402.
https://doi.org/10.1103/PhysRevLett.119.040402
[17] S. Sarkar, D. Saha, J. Kaniewski, and R. Augusiak. Self-testing quantum systems of arbitrary local dimension with minimal number of measurements. arXiv:1909.12722 [quant-ph], 2019.
arXiv:1909.12722
[18] V. B. Scholz and R. F. Werner. Tsirelson's problem. arXiv:0812.4305, 2008.
arXiv:0812.4305
[19] W. Slofstra. The set of quantum correlations is not closed. Forum of Mathematics, Pi, 7: E1, 2019. 10.1017/fmp.2018.3.
https://doi.org/10.1017/fmp.2018.3
[20] W. Slofstra. Tsirelson's problem and an embedding theorem for groups arising from non-local games. Journal of the American Mathematical Society, 33: 1–56, 2020. 10.1090/jams/929.
https://doi.org/10.1090/jams/929
[21] W. van Dam and P. Hayden. Universal entanglement transformations without communication. Physical Review A, 67 (6): 060302, 2003. 10.1103/PhysRevA.67.060302.
https://doi.org/10.1103/PhysRevA.67.060302
[22] T. Haur Yang and M. Navascués. Robust self-testing of unknown quantum systems into any entangled two-qubit states. Physical Review A, 87 (5): 050102, 2013. 10.1103/PhysRevA.87.050102.
https://doi.org/10.1103/PhysRevA.87.050102
Cited by
[1] Shubhayan Sarkar and Remigiusz Augusiak, "Self-testing of multipartite Greenberger-Horne-Zeilinger states of arbitrary local dimension with arbitrary number of measurements per party", Physical Review A 105 3, 032416 (2022).
[2] Shubhayan Sarkar, "Certification of entangled quantum states and quantum measurements in Hilbert spaces of arbitrary dimension", arXiv:2302.01325, (2023).
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