Quantum Correlations On The No-signaling Boundary: Self-testing And More

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Kai-Siang Chen¹, Gelo Noel M. Tabia^1,2,3, Chellasamy Jebarathinam^4,5, Shiladitya Mal^1,2, Jun-Yi Wu⁶, and Yeong-Cherng Liang^1,2

¹Department of Physics and Center for Quantum Frontiers of Research & Technology (QFort), National Cheng Kung University, Tainan 701, Taiwan
²Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan
³Center for Quantum Technology, National Tsing Hua University, Hsinchu 300, Taiwan
⁴Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
⁵Department of Physics and Center for Quantum Information Science, National Cheng Kung University, Tainan 70101, Taiwan
⁶Department of Physics, Tamkang University, Tamsui, New Taipei 251301, Taiwan

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Abstract

In device-independent quantum information, correlations between local measurement outcomes observed by spatially separated parties in a Bell test play a fundamental role. Even though it is long-known that the set of correlations allowed in quantum theory lies strictly between the Bell-local set and the no-signaling set, many questions concerning the geometry of the quantum set remain unanswered. Here, we revisit the problem of when the boundary of the quantum set coincides with the no-signaling set in the simplest Bell scenario. In particular, for each Class of these common boundaries containing $k$ zero probabilities, we provide a $(5-k)$-parameter family of quantum strategies realizing these (extremal) correlations. We further prove that self-testing is possible in all nontrivial Classes beyond the known examples of Hardy-type correlations, and provide numerical evidence supporting the robustness of these self-testing results. Candidates of one-parameter families of self-testing correlations from some of these Classes are identified. As a byproduct of our investigation, if the qubit strategies leading to an extremal nonlocal correlation are local-unitarily equivalent, a self-testing statement provably follows. Interestingly, all these self-testing correlations found on the no-signaling boundary are provably non-exposed. An analogous characterization for the set $mathcal{M}$ of quantum correlations arising from finite-dimensional maximally entangled states is also provided. En route to establishing this last result, we show that all correlations of $mathcal{M}$ in the simplest Bell scenario are attainable as convex combinations of those achievable using a Bell pair and projective measurements. In turn, we obtain the maximal Clauser-Horne-Shimony-Holt Bell inequality violation by any maximally entangled two-qudit state and a no-go theorem regarding the self-testing of such states.

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Featured image: A two-dimensional projection of the no-signaling set $mathcal{NS}$, an outer approximation $tilde{Q}$ of the quantum set, and the local set $mathcal{L}$ of correlations. All (quantum) correlations having the three zero entries $P(0,0|0,0)=P(1,1|0,0)=P(1,0|1,1)=0$ lie on the vertical line where the horizontal value is zero. Among them, $vec{P}_{mathcal{Q}}$ gives the maximal $mathcal{S}_{text{CHSH}}$ value and self-tests a quantum strategy.

► BibTeX data

@article{Chen2023quantumcorrelations, doi = {10.22331/q-2023-07-11-1054}, url = {https://doi.org/10.22331/q-2023-07-11-1054}, title = {Quantum correlations on the no-signaling boundary: self-testing and more}, author = {Chen, Kai-Siang and Tabia, Gelo Noel M. and Chellasamy Jebarathinam and Mal, Shiladitya and Wu, Jun-Yi and Liang, Yeong-Cherng}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {1054}, month = jul, year = {2023}<br /> }

► References

[1] S. Popescu and D. Rohrlich, Found. Phys. 24, 379 (1994).
https://doi.org/10.1007/BF02058098

[2] G. Brassard, H. Buhrman, N. Linden, A. A. Méthot, A. Tapp, and F. Unger, Phys. Rev. Lett. 96, 250401 (2006).
https://doi.org/10.1103/PhysRevLett.96.250401

[3] M. Navascués and H. Wunderlich, Proc. R. Soc. A 466, 881 (2009).
https://doi.org/10.1098/rspa.2009.0453

[4] M. Pawlowski, T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter, and M. Zukowski, Nature 461, 1101 (2009).
https://doi.org/10.1038/nature08400

[5] M. Navascués, Y. Guryanova, M. J. Hoban, and A. Acín, Nat. Commun. 6, 6288 (2015).
https://doi.org/10.1038/ncomms7288

[6] J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy, 2nd ed. (Cambridge University Press, 2004).
https://doi.org/10.1017/CBO9780511815676

[7] T. Norsen, Am. J. Phys. 79, 1261 (2011).
https://doi.org/10.1119/1.3630940

[8] J. S. Bell, Physics 1, 195 (1964).
https://doi.org/10.1103/PhysicsPhysiqueFizika.1.195

[9] N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, Rev. Mod. Phys. 86, 419 (2014).
https://doi.org/10.1103/RevModPhys.86.419

[10] V. Scarani, Acta Physica Slovaca 62, 347 (2012).

[11] A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, Phys. Rev. Lett. 98, 230501 (2007).
https://doi.org/10.1103/PhysRevLett.98.230501

[12] R. Colbeck, PhD thesis, arXiv:0911.3814 (2009).
https://doi.org/10.48550/arXiv.0911.3814
arXiv:0911.3814

[13] S. Pironio, A. Acín, S. Massar, A. B. d. l. Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, Nature 464, 1021 (2010).
https://doi.org/10.1038/nature09008

[14] R. Gallego, N. Brunner, C. Hadley, and A. Acín, Phys. Rev. Lett. 105, 230501 (2010).
https://doi.org/10.1103/PhysRevLett.105.230501

[15] J.-D. Bancal, N. Gisin, Y.-C. Liang, and S. Pironio, Phys. Rev. Lett. 106, 250404 (2011).
https://doi.org/10.1103/PhysRevLett.106.250404

[16] T. Moroder, J.-D. Bancal, Y.-C. Liang, M. Hofmann, and O. Gühne, Phys. Rev. Lett. 111, 030501 (2013).
https://doi.org/10.1103/PhysRevLett.111.030501

[17] Y.-C. Liang, D. Rosset, J.-D. Bancal, G. Pütz, T. J. Barnea, and N. Gisin, Phys. Rev. Lett. 114, 190401 (2015).
https://doi.org/10.1103/PhysRevLett.114.190401

[18] S.-L. Chen, C. Budroni, Y.-C. Liang, and Y.-N. Chen, Phys. Rev. Lett. 116, 240401 (2016).
https://doi.org/10.1103/PhysRevLett.116.240401

[19] F. Baccari, D. Cavalcanti, P. Wittek, and A. Acín, Phys. Rev. X 7, 021042 (2017).
https://doi.org/10.1103/PhysRevX.7.021042

[20] J.-D. Bancal, N. Sangouard, and P. Sekatski, Phys. Rev. Lett. 121, 250506 (2018).
https://doi.org/10.1103/PhysRevLett.121.250506

[21] M. Zwerger, W. Dür, J.-D. Bancal, and P. Sekatski, Phys. Rev. Lett. 122, 060502 (2019).
https://doi.org/10.1103/PhysRevLett.122.060502

[22] P. Sekatski, J.-D. Bancal, S. Wagner, and N. Sangouard, Phys. Rev. Lett. 121, 180505 (2018).
https://doi.org/10.1103/PhysRevLett.121.180505

[23] S.-L. Chen, C. Budroni, Y.-C. Liang, and Y.-N. Chen, Phys. Rev. A 98, 042127 (2018).
https://doi.org/10.1103/PhysRevA.98.042127

[24] R. Arnon-Friedman and J.-D. Bancal, New J. Phys. 21, 033010 (2019).
https://doi.org/10.1088/1367-2630/aafef6

[25] S. Wagner, J.-D. Bancal, N. Sangouard, and P. Sekatski, Quantum 4, 243 (2020).
https://doi.org/10.22331/q-2020-03-19-243

[26] S.-L. Chen, H.-Y. Ku, W. Zhou, J. Tura, and Y.-N. Chen, Quantum 5, 552 (2021).
https://doi.org/10.22331/q-2021-09-28-552

[27] A. Gočanin, I. Šupić, and B. Dakić, PRX Quantum 3, 010317 (2022).
https://doi.org/10.1103/PRXQuantum.3.010317

[28] Y.-C. Liang and Y. Zhang, Entropy 21 (2019).
https://doi.org/10.3390/e21020185

[29] D. Mayers and A. Yao, Quantum Info. Comput. 4, 273 (2004).

[30] I. Šupić and J. Bowles, Quantum 4, 337 (2020).
https://doi.org/10.22331/q-2020-09-30-337

[31] J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, Science 360, 285 (2018).
https://doi.org/10.1126/science.aar7053

[32] W.-H. Zhang, G. Chen, X.-X. Peng, X.-J. Ye, P. Yin, X.-Y. Xu, J.-S. Xu, C.-F. Li, and G.-C. Guo, Phys. Rev. Lett. 122, 090402 (2019a).
https://doi.org/10.1103/PhysRevLett.122.090402

[33] W.-H. Zhang, G. Chen, P. Yin, X.-X. Peng, X.-M. Hu, Z.-B. Hou, Z.-Y. Zhou, S. Yu, X.-J. Ye, Z.-Q. Zhou, X.-Y. Xu, J.-S. Tang, J.-S. Xu, Y.-J. Han, B.-H. Liu, C.-F. Li, and G.-C. Guo, Npj Quantum Inf. 5, 4 (2019b).
https://doi.org/10.1038/s41534-018-0120-0

[34] S. Gómez, A. Mattar, I. Machuca, E. S. Gómez, D. Cavalcanti, O. J. Farías, A. Acín, and G. Lima, Phys. Rev. A 99, 032108 (2019).
https://doi.org/10.1103/PhysRevA.99.032108

[35] J.-D. Bancal, K. Redeker, P. Sekatski, W. Rosenfeld, and N. Sangouard, Quantum 5, 401 (2021).
https://doi.org/10.22331/q-2021-03-02-401

[36] D. Wu, Q. Zhao, C. Wang, L. Huang, Y.-F. Jiang, B. Bai, Y. Zhou, X.-M. Gu, F.-M. Liu, Y.-Q. Mao, Q.-C. Sun, M.-C. Chen, J. Zhang, C.-Z. Peng, X.-B. Zhu, Q. Zhang, C.-Y. Lu, and J.-W. Pan, Phys. Rev. Lett. 128, 250401 (2022).
https://doi.org/10.1103/PhysRevLett.128.250401

[37] J. Barrett, N. Linden, S. Massar, S. Pironio, S. Popescu, and D. Roberts, Phys. Rev. A 71, 022101 (2005).
https://doi.org/10.1103/PhysRevA.71.022101

[38] P. Horodecki and R. Ramanathan, Nat. Commun. 10, 1701 (2019).
https://doi.org/10.1038/s41467-019-09505-2

[39] P. M. Pearle, Phys. Rev. D 2, 1418 (1970).
https://doi.org/10.1103/PhysRevD.2.1418

[40] S. L. Braunstein and C. M. Caves, Ann. Phys. 202, 22 (1990).
https://doi.org/10.1016/0003-4916(90)90339-P

[41] J. Barrett, A. Kent, and S. Pironio, Phys. Rev. Lett. 97, 170409 (2006).
https://doi.org/10.1103/PhysRevLett.97.170409

[42] K. T. Goh, J. Kaniewski, E. Wolfe, T. Vértesi, X. Wu, Y. Cai, Y.-C. Liang, and V. Scarani, Phys. Rev. A 97, 022104 (2018).
https://doi.org/10.1103/PhysRevA.97.022104

[43] R. Colbeck and R. Renner, Nat. Commun. 2, 411 (2011).
https://doi.org/10.1038/ncomms1416

[44] R. Colbeck and R. Renner, Nat. Phys. 8, 450 (2012).
https://doi.org/10.1038/nphys2300

[45] G. Pütz, D. Rosset, T. J. Barnea, Y.-C. Liang, and N. Gisin, Phys. Rev. Lett. 113, 190402 (2014).
https://doi.org/10.1103/PhysRevLett.113.190402

[46] M. Kessler and R. Arnon-Friedman, IEEE J. Sel. Areas Commun. 1, 568 (2020).
https://doi.org/10.1109/JSAIT.2020.3012498

[47] L. Hardy, Phys. Rev. Lett. 71, 1665 (1993).
https://doi.org/10.1103/PhysRevLett.71.1665

[48] R. Ramanathan, M. Horodecki, H. Anwer, S. Pironio, K. Horodecki, M. Grünfeld, S. Muhammad, M. Bourennane, and P. Horodecki, arXiv:1810.11648 (2018).
https://doi.org/10.48550/arXiv.1810.11648
arXiv:1810.11648

[49] A. Rai, C. Duarte, S. Brito, and R. Chaves, Phys. Rev. A 99, 032106 (2019).
https://doi.org/10.1103/PhysRevA.99.032106

[50] R. Rabelo, L. Y. Zhi, and V. Scarani, Phys. Rev. Lett. 109, 180401 (2012).
https://doi.org/10.1103/PhysRevLett.109.180401

[51] S. Kunkri, S. K. Choudhary, A. Ahanj, and P. Joag, Phys. Rev. A 73, 022346 (2006).
https://doi.org/10.1103/PhysRevA.73.022346

[52] L.-M. Liang and C.-Z. Li, Phys. Lett. A 335, 371 (2005).
https://doi.org/10.1016/j.physleta.2004.12.046

[53] A. Rai, M. Pivoluska, M. Plesch, S. Sasmal, M. Banik, and S. Ghosh, Phys. Rev. A 103, 062219 (2021).
https://doi.org/10.1103/PhysRevA.103.062219

[54] A. Rai, M. Pivoluska, S. Sasmal, M. Banik, S. Ghosh, and M. Plesch, Phys. Rev. A 105, 052227 (2022).
https://doi.org/10.1103/PhysRevA.105.052227

[55] J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).
https://doi.org/10.1103/PhysRevLett.23.880

[56] D. Collins and N. Gisin, J. Phys. A: Math. Gen. 37, 1775 (2004).
https://doi.org/10.1088/0305-4470/37/5/021

[57] A. Peres, Found. Phys. 20, 1441 (1990).
https://doi.org/10.1007/BF01883517

[58] Y.-C. Liang, T. Vértesi, and N. Brunner, Phys. Rev. A 83, 022108 (2011a).
https://doi.org/10.1103/PhysRevA.83.022108

[59] T. Vidick and S. Wehner, Phys. Rev. A 83, 052310 (2011).
https://doi.org/10.1103/PhysRevA.83.052310

[60] M. Junge and C. Palazuelos, Commun. Math. Phys. 306, 695 (2011).
https://doi.org/10.1007/s00220-011-1296-8

[61] B. G. Christensen, Y.-C. Liang, N. Brunner, N. Gisin, and P. G. Kwiat, Phys. Rev. X 5, 041052 (2015).
https://doi.org/10.1103/PhysRevX.5.041052

[62] P.-S. Lin, T. Vértesi, and Y.-C. Liang, Quantum 6, 765 (2022).
https://doi.org/10.22331/q-2022-07-14-765

[63] C. Jebarathinam, J.-C. Hung, S.-L. Chen, and Y.-C. Liang, Phys. Rev. Research 1, 033073 (2019).
https://doi.org/10.1103/PhysRevResearch.1.033073

[64] J. Kaniewski, Phys. Rev. Research 2, 033420 (2020).
https://doi.org/10.1103/PhysRevResearch.2.033420

[65] N. Gigena and J. Kaniewski, Phys. Rev. A 106, 012401 (2022).
https://doi.org/10.1103/PhysRevA.106.012401

[66] L. Masanes, Phys. Rev. Lett. 97, 050503 (2006).
https://doi.org/10.1103/PhysRevLett.97.050503

[67] T. Franz, F. Furrer, and R. F. Werner, Phys. Rev. Lett. 106, 250502 (2011).
https://doi.org/10.1103/PhysRevLett.106.250502

[68] L. Mančinska and S. Wehner, J. Phys. A: Math. Theo. 47, 424027 (2014).
https://doi.org/10.1088/1751-8113/47/42/424027

[69] T. Fritz, Found. Phys. 41, 1493 (2011).
https://doi.org/10.1007/s10701-011-9563-2

[70] K. F. Pál and T. Vértesi, Phys. Rev. A 80, 042114 (2009).
https://doi.org/10.1103/PhysRevA.80.042114

[71] J. M. Donohue and E. Wolfe, Phys. Rev. A 92, 062120 (2015).
https://doi.org/10.1103/PhysRevA.92.062120

[72] Y.-C. Liang, Correlations, Bell Inequality Violation & Quantum Entanglement, Ph.D. thesis, University of Queensland (2008).
https://doi.org/10.48550/arXiv.0810.5400

[73] R. F. Werner, Phys. Rev. A 40, 4277 (1989).
https://doi.org/10.1103/PhysRevA.40.4277

[74] Y.-C. Liang, R. W. Spekkens, and H. M. Wiseman, Phys. Rep. 506, 1 (2011b).
https://doi.org/10.1016/j.physrep.2011.05.001

[75] A. Fine, Phys. Rev. Lett. 48, 291 (1982).
https://doi.org/10.1103/PhysRevLett.48.291

[76] Y. Xiang, Chin. Phys. B 20, 060301 (2011).
https://doi.org/10.1088/1674-1056/20/6/060301

[77] T. H. Yang, T. Vértesi, J.-D. Bancal, V. Scarani, and M. Navascués, Phys. Rev. Lett. 113, 040401 (2014).
https://doi.org/10.1103/PhysRevLett.113.040401

[78] J.-D. Bancal, M. Navascués, V. Scarani, T. Vértesi, and T. H. Yang, Phys. Rev. A 91, 022115 (2015).
https://doi.org/10.1103/PhysRevA.91.022115

[79] T. F. Jordan, Phys. Rev. A 50, 62 (1994).
https://doi.org/10.1103/PhysRevA.50.62

[80] M. T. Quintino, M. Araújo, D. Cavalcanti, M. F. Santos, and M. T. Cunha, J. Phys. A: Math. Theo. 45, 215308 (2012).
https://doi.org/10.1088/1751-8113/45/21/215308

[81] Y. Wang, X. Wu, and V. Scarani, New J. Phys. 18, 025021 (2016).
https://doi.org/10.1088/1367-2630/18/2/025021

[82] K.-S. Chen et al., “Generalizing Hardy’s paradox by means of the failure of transitivity of implications,” (in preparation).

[83] A. Cabello, Phys. Rev. A 65, 032108 (2002).
https://doi.org/10.1103/PhysRevA.65.032108

[84] R. Cleve, P. Hoyer, B. Toner, and J. Watrous, in Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004. (2004) pp. 236–249.
https://doi.org/10.1109/CCC.2004.1313847

[85] Y.-C. Liang and A. C. Doherty, Phys. Rev. A 75, 042103 (2007).
https://doi.org/10.1103/PhysRevA.75.042103

[86] G. M. D’Ariano, P. L. Presti, and P. Perinotti, J. Phys. A: Math. Gen. 38, 5979 (2005).
https://doi.org/10.1088/0305-4470/38/26/010

[87] W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
https://doi.org/10.1103/PhysRevLett.80.2245

[88] Y.-C. Liang and A. C. Doherty, Phys. Rev. A 73, 052116 (2006).
https://doi.org/10.1103/PhysRevA.73.052116

[89] J. Kaniewski, Phys. Rev. Lett. 117, 070402 (2016).
https://doi.org/10.1103/PhysRevLett.117.070402

[90] T. P. Le, C. Meroni, B. Sturmfels, R. F. Werner, and T. Ziegler, Quantum 7, 947 (2023).
https://doi.org/10.22331/q-2023-03-16-947

[91] J. Kaniewski, (private communication).

[92] J.-L. Chen, A. Cabello, Z.-P. Xu, H.-Y. Su, C. Wu, and L. C. Kwek, Phys. Rev. A 88, 062116 (2013).
https://doi.org/10.1103/PhysRevA.88.062116

[93] M. Navascués, S. Pironio, and A. Acín, New J. Phys. 10, 073013 (2008).
https://doi.org/10.1088/1367-2630/10/7/073013

[94] A. C. Doherty, Y.-C. Liang, B. Toner, and S. Wehner, in 23rd Annu. IEEE Conf. on Comput. Comp, 2008, CCC’08 (Los Alamitos, CA, 2008) pp. 199–210.
https://doi.org/10.1109/CCC.2008.26

[95] S. L. Braunstein, A. Mann, and M. Revzen, Phys. Rev. Lett. 68, 3259 (1992).
https://doi.org/10.1103/PhysRevLett.68.3259

[96] S. Boyd and L. Vandenberghe, Convex Optimization, 1st ed. (Cambridge University Press, Cambridge, 2004).

Cited by

[1] Antoni Mikos-Nuszkiewicz and Jędrzej Kaniewski, “Extremal points of the quantum set in the CHSH scenario: conjectured analytical solution”, arXiv:2302.10658, (2023).

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Source: https://quantum-journal.org/papers/q-2023-07-11-1054/

Time Stamp: July 11, 2023

Time Stamp: Oct 10, 2023

Quantum correlations on the no-signaling boundary: self-testing and more

Republished By Plato

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