ন্যূনতম দৃশ্যকল্পে কোয়ান্টাম পারস্পরিক সম্পর্ক

[1] Alain Aspect, Philippe Grangier, and Gérard Roger. ``Experimental realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A new violation of Bell's inequalities''. Phys. Rev. Lett. 49, 91–94 (1982).
https: / / doi.org/ 10.1103 / ফিজিরভাইলেট .49.91

[2] B. Hensen, R. Hanson, et al. ``Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres''. Nature 526, 682 EP – (2015). arXiv:1508.05949.
https: / / doi.org/ 10.1038 / nature15759
arXiv: 1508.05949

[3] N. Sangouard, J.-D. Bancal, N. Gisin, W. Rosenfeld, P. Sekatski, M. Weber, and H. Weinfurter. ``Loophole-free Bell test with one atom and less than one photon on average''. Phys. Rev. A 84, 052122 (2011). arXiv:1108.1027.
https: / / doi.org/ 10.1103 / ফিজারিভা 84.052122
arXiv: 1108.1027

[4] J. S. Bell. ``On the Einstein Podolsky Rosen paradox''. Physics 1, 195–200 (1964).
https: / / doi.org/ 10.1103 / পদার্থবিজ্ঞান ফিজিকফিজিকা.1.195 XNUMX

[5] জন এফ. ক্লজার, মাইকেল এ. হর্ন, আবনার শিমনি এবং রিচার্ড এ. হল্ট। ''স্থানীয় লুকানো পরিবর্তনশীল তত্ত্বগুলি পরীক্ষা করার জন্য প্রস্তাবিত পরীক্ষা''। ফিজ। রেভ. লেট। 23, 880-884 (1969)।
https: / / doi.org/ 10.1103 / ফিজিরভাইলেট .23.880

[6] R. F. Werner et al. ``Open quantum problems''. url: https:/​/​oqp.iqoqi.oeaw.ac.at/​.
https://​oqp.iqoqi.oeaw.ac.at/​

[7] Boris S. Tsirelson. ``Quantum analogues of the Bell inequalities. the case of two spatially separated domains''. J. Soviet Math. 36, 557–570 (1987).
https: / / doi.org/ 10.1007 / BF01663472

[8] R. F. Werner and M. M. Wolf. ``All multipartite Bell-correlation inequalities for two dichotomic observables per site''. Phys. Rev. A 64, 032112 (2001). arXiv:quant-ph/​0102024.
https: / / doi.org/ 10.1103 / ফিজারিভা 64.032112
আরএক্সিভ: কোয়ান্ট-পিএইচ / 0102024

[9] William Slofstra. ``The set of quantum correlations is not closed''. Forum of Mathematics, Pi 7, e1 (2019). arXiv:1703.08618.
https://​/​doi.org/​10.1017/​fmp.2018.3
arXiv: 1703.08618

[10] Volkher B. Scholz and R. F. Werner. ``Tsirelson's problem'' (2008). arXiv:0812.4305.
arXiv: 0812.4305

[11] Boris S Tsirelson. ``Some results and problems on quantum Bell-type inequalities''. Hadronic Journal Supplement 8, 329–345 (1993). url: https:/​/​www.tau.ac.il/​ tsirel/​download/​hadron.html.
https://​/​www.tau.ac.il/​~tsirel/​download/​hadron.html

[12] Miguel Navascues, Stefano Pironio, and Antonio Acín. ``A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations''. New J. Phys. 10, 073013 (2008).
https:/​/​doi.org/​10.1088/​1367-2630/​10/​7/​073013

[13] M. Junge, M. Navascues, C. Palazuelos, D. Perez-Garcia, V. B. Scholz, and R. F. Werner. ``Connes' embedding problem and Tsirelson's problem''. J. Math. Phys. 52, 012102 (2011). arXiv:1008.1142.
https: / / doi.org/ 10.1063 / 1.3514538
arXiv: 1008.1142

[14] Tobias Fritz. ``Tsirelson's problem and Kirchberg's conjecture''. Rev. Math. Phys. 24, 1250012 (2012). arXiv:1008.1168.
https://​doi.org/​10.1142/​S0129055X12500122
arXiv: 1008.1168

[15] Zhengfeng Ji, Anand Natarajan, Thomas Vidick, John Wright, and Henry Yuen. ``MIP*=RE'' (2020). arXiv:2001.04383.
arXiv: 2001.04383

[16] Günther M. Ziegler. ``Lectures on polytopes''. Springer. Berlin (1995).
https:/​/​doi.org/​10.1007/​978-1-4613-8431-1

[17] Mateusz Michałek and Bernd Sturmfels. ``Invitation to nonlinear algebra''. Volume 211 of Graduate Studies in Mathematics. AMS. (2021).
https://​doi.org/​10.1007/​s00591-022-00324-z

[18] Grigoriy Blekherman, Pablo Parrilo, and Rekha Thomas. ``Semidefinite optimization and convex algebraic geometry''. MOS-SIAM Series on Optimization 13. SIAM. Philadelphia (2012).
https: / / doi.org/ 10.1137 / 1.9781611972290

[19] Bernd Sturmfels and Caroline Uhler. ``Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry''. Ann. Inst. Statist. Math. 62, 603–638 (2010). arXiv:0906.3529.
https:/​/​doi.org/​10.1007/​s10463-010-0295-4
arXiv: 0906.3529

[20] Claus Scheiderer. ``Spectrahedral shadows''. SIAM J. Appl. Algebra Geometry 2, 26–44 (2018). arXiv:1612.07048.
https://​doi.org/​10.1137/​17M1118981
arXiv: 1612.07048

[21] B. S. Cirel'son. ``Quantum generalizations of Bell's inequality''. Lett. Math. Phys. 4, 93–100 (1980).
https: / / doi.org/ 10.1007 / BF00417500

[22] Jukka Kiukas and Reinhard F. Werner. ``Maximal violation of Bell inequalities by position measurements''. J. Math. Phys. 51, 072105 (2010). arXiv:0912.3740.
https: / / doi.org/ 10.1063 / 1.3447736
arXiv: 0912.3740

[23] Lawrence J. Landau. ``Empirical two-point correlation functions''. Found. Phys. 18, 449–460 (1988).
https: / / doi.org/ 10.1007 / BF00732549

[24] L Masanes. ``Necessary and sufficient condition for quantum-generated correlations'' (2003) arXiv:quant-ph/​0309137.
আরএক্সিভ: কোয়ান্ট-পিএইচ / 0309137

[25] Yukun Wang, Xingyao Wu, and Valerio Scarani. ``All the self-testings of the singlet for two binary measurements''. New J. Phys. 18, 025021 (2016). arXiv:1511.04886.
https:/​/​doi.org/​10.1088/​1367-2630/​18/​2/​025021
arXiv: 1511.04886

[26] Andrew C Doherty, Yeong-Cherng Liang, Ben Toner, and Stephanie Wehner. ``The quantum moment problem and bounds on entangled multi-prover games''. In 23rd Annual IEEE Conference on Computational Complexity. Pages 199–210. IEEE (2008). arXiv:0803.4373.
https://​doi.org/​10.1109/CCC.2008.26
arXiv: 0803.4373

[27] Tobias Fritz. ``Polyhedral duality in Bell scenarios with two binary observables''. J. Math. Phys. 53, 072202 (2012). arXiv:1202.0141.
https: / / doi.org/ 10.1063 / 1.4734586
arXiv: 1202.0141

[28] Dominic Mayers and Andrew Yao. ``Self testing quantum apparatus''. Quantum Info. Comput. 4, 273–286 (2004). arXiv:quant-ph/​0307205.
https://​doi.org/​10.26421/​QIC4.4-3
আরএক্সিভ: কোয়ান্ট-পিএইচ / 0307205

[29] Stephen J. Summers and Reinhard F. Werner. ``Maximal violation of Bell's inequalities is generic in quantum field theory''. Commun. Math. Phys. 110, 247–259 (1987).
https: / / doi.org/ 10.1007 / BF01207366

[30] L Masanes. ``Extremal quantum correlations for n parties with two dichotomic observables per site'' (2005) arXiv:quant-ph/​0512100.
আরএক্সিভ: কোয়ান্ট-পিএইচ / 0512100

[31] Le Phuc Thinh, Antonios Varvitsiotis, and Yu Cai. ``Geometric structure of quantum correlators via semidefinite programming''. Phys. Rev. A 99, 052108 (2019). arXiv:1809.10886.
https: / / doi.org/ 10.1103 / ফিজারিভা 99.052108
arXiv: 1809.10886

[32] Nicolas Brunner, Daniel Cavalcanti, Stefano Pironio, Valerio Scarani, and Stephanie Wehner. ``Bell nonlocality''. Rev. Mod. Phys. 86, 419–478 (2014). arXiv:1303.2849.
https: / / doi.org/ 10.1103 / RevModPhys.86.419
arXiv: 1303.2849

[33] Koon Tong Goh, Jędrzej Kaniewski, Elie Wolfe, Tamás Vértesi, Xingyao Wu, Yu Cai, Yeong-Cherng Liang, and Valerio Scarani. ``Geometry of the set of quantum correlations''. Phys. Rev. A 97, 022104 (2018). arXiv:1710.05892.
https: / / doi.org/ 10.1103 / ফিজারিভা 97.022104
arXiv: 1710.05892

[34] Ivan Šupić and Joseph Bowles. ``Self-testing of quantum systems: a review''. Quantum 4, 337 (2020). arXiv:1904.10042.
https:/​/​doi.org/​10.22331/​q-2020-09-30-337
arXiv: 1904.10042

[35] Rene Schwonnek, Koon Tong Goh, Ignatius W. Primaatmaja, Ernest Y. Z. Tan, Ramona Wolf, Valerio Scarani, and Charles C. W. Lim. ``Device-independent quantum key distribution with random key basis''. Nat. Commun. 12, 2880 (2020). arXiv:2005.02691.
https:/​/​doi.org/​10.1038/​s41467-021-23147-3
arXiv: 2005.02691

[36] Ernest Y. Z. Tan, René Schwonnek, Koon Tong Goh, Ignatius William Primaatmaja, and Charles C. W. Lim. ``Computing secure key rates for quantum key distribution with untrusted devices''. npj Quantum Inf. 7, 158 (2021). arXiv:1908.11372.
https://​doi.org/​10.1038/​s41534-021-00494-z
arXiv: 1908.11372

[37] K. G. H. Vollbrecht and R. F. Werner. ``Entanglement measures under symmetry''. Phys. Rev. A 64, 062307 (2001). arXiv:quant-ph/​0010095.
https: / / doi.org/ 10.1103 / ফিজারিভা 64.062307
আরএক্সিভ: কোয়ান্ট-পিএইচ / 0010095

[38] Peter Bierhorst. ``Geometric decompositions of Bell polytopes with practical applications''. J. Phys. A 49, 215301 (2016). arXiv:1511.04127.
https:/​/​doi.org/​10.1088/​1751-8113/​49/​21/​215301
arXiv: 1511.04127

[39] Monique Laurent. ``The real positive semidefinite completion problem for series-parallel graphs''. Linear Algebra and its Applications 252, 347–366 (1997).
https:/​/​doi.org/​10.1016/​0024-3795(95)00741-5

[40] Vaughan F. R. Jones and J. H. Przytycki. ``Lissajous knots and billiard knots''. Banach Cent. Pub. 42, 145–163 (1998).
https:/​/​doi.org/​10.4064/​-42-1-145-163

[41] Kaie Kubjas, Pablo A Parrilo, and Bernd Sturmfels. ``How to flatten a soccer ball''. In Aldo Conca, Joseph Gubeladze, and Tim Römer, editors, Homological and Computational Methods in Commutative Algebra. Volume 20 of INdAM Ser., pages 141–162. Springer (2017).
https:/​/​doi.org/​10.1007/​978-3-319-61943-9_9

[42] Kathleen S. Gibbons, Matthew J. Hoffman, and William K. Wootters. ``Discrete phase space based on finite fields''. Phys. Rev. A 70, 062101 (2004). arXiv:quant-ph/​0401155.
https: / / doi.org/ 10.1103 / physreva.70.062101
আরএক্সিভ: কোয়ান্ট-পিএইচ / 0401155

[43] Reinhard F. Werner. ``Uncertainty relations for general phase spaces''. Frontiers of Physics 11, 1–10 (2016). arXiv:arxiv:1601.03843.
https:/​/​doi.org/​10.1007/​s11467-016-0558-5
arXiv: 1601.03843

[44] Amritanshu Prasad, Ilya Shapiro, and M.K. Vemuri. ``Locally compact abelian groups with symplectic self-duality''. Adv. Math. 225, 2429–2454 (2010). arXiv:0906.4397.
https://​doi.org/​10.1016/​j.aim.2010.04.023
arXiv: 0906.4397

[45] Daniel Ciripoi, Nidhi Kaihnsa, Andreas Löhne, and Bernd Sturmfels. ``Computing convex hulls of trajectories''. Rev. Un. Mat. Argentina 60, 637–662 (2019). arXiv:1810.03547.
https://​doi.org/​10.33044/​revuma.v60n2a22
arXiv: 1810.03547

[46] Daniel Plaumann, Rainer Sinn, and Jannik Lennart Wesner. ``Families of faces and the normal cycle of a convex semi-algebraic set''. Beitr. Algebra Geom. (2022). arXiv:2104.13306.
https:/​/​doi.org/​10.1007/​s13366-022-00657-9
arXiv: 2104.13306

[47] Daniel R. Grayson and Michael E. Stillman. ``Macaulay2, a software system for research in algebraic geometry''. Available at http:/​/​www.math.uiuc.edu/​Macaulay2/​.
http://​/​www.math.uiuc.edu/​Macaulay2/​

[48] John Ottem, Kristian Ranestad, Bernd Sturmfels, and Cynthia Vinzant. ``Quartic spectrahedra''. Mathematical Programming, Ser. B 151, 585–612 (2015). arXiv:1311.3675.
https:/​/​doi.org/​10.1007/​s10107-014-0844-3
arXiv: 1311.3675

[49] Adán Cabello. ``How much larger quantum correlations are than classical ones''. Phys. Rev. A 72, 012113 (2005). arXiv:quant-ph/​0409192.
https: / / doi.org/ 10.1103 / ফিজারিভা 72.012113
আরএক্সিভ: কোয়ান্ট-পিএইচ / 0409192

[50] C. E. González-Guillén, C. H. Jiménez, C. Palazuelos, and I. Villanueva. ``Sampling quantum nonlocal correlations with high probability''. Commun. Math. Phys. 344, 141–154 (2016). arXiv:1412.4010.
https:/​/​doi.org/​10.1007/​s00220-016-2625-8
arXiv: 1412.4010

[51] C. R. Johnson and G. Nævdal. ``The probability that a (partial) matrix is positive semidefinite''. In I. Gohberg, R. Mennicken, and C. Tretter, editors, Recent Progress in Operator Theory. Pages 171–182. Basel (1998). Birkhäuser Basel.
https:/​/​doi.org/​10.1007/​978-3-0348-8793-9_10

[52] H. H Schaefer and M. P Wolff. ``Topological vector spaces''. Springer. (1999).
https:/​/​doi.org/​10.1007/​978-1-4612-1468-7

[53] Wojciech Tadej and Karol Z̀yczkowski. ``A concise guide to complex Hadamard matrices''. Open Systems & Information Dynamics 13, 133–177 (2006). arXiv:quant-ph/​0512154.
https:/​/​doi.org/​10.1007/​s11080-006-8220-2
আরএক্সিভ: কোয়ান্ট-পিএইচ / 0512154

[54] H. Barnum, C.P. Gaebler, and A. Wilce. ``Ensemble steering, weak self-duality, and the structure of probabilistic theories''. Found. Phys 43, 1411–1427 (2013). arXiv:0912.5532.
https:/​/​doi.org/​10.1007/​s10701-013-9752-2
arXiv: 0912.5532

[55] Nikos Yannakakis. ``Stampacchia's property, self-duality and orthogonality relations''. Set-Valued and Variational Analysis 19, 555–567 (2011). arXiv:1008.4958.
https: / / doi.org/ 10.1007 / s11228-011-0175-y
arXiv: 1008.4958

[56] Jacek Bochnak, Michel Coste, and Marie-Françoise Roy. ``Real algebraic geometry''. Volume 36 of A Series of Modern Surveys in Mathematics. Springer Berlin, Heidelberg. (2013).
https:/​/​doi.org/​10.1007/​978-3-662-03718-8

[57] Joseph H. G. Fu. ``Algebraic integral geometry''. Pages 47–112. Springer Basel. Basel (2014). arXiv:1103.6256.
https:/​/​doi.org/​10.1007/​978-3-0348-0874-3_2
arXiv: 1103.6256

[58] Herbert Federer. ``Curvature measures''. Trans. Amer. Math. Soc. 93, 418–491 (1959).
https: / / doi.org/ 10.2307 / 1993504

[59] Peter Wintgen. ``Normal cycle and integral curvature for polyhedra in Riemannian manifolds''. In Gy. Soos and J. Szenthe, editors, Differential Geometry. Volume 21. North-Holland, Amsterdam (1982).

[60] Martina Zähle. ``Integral and current representation of Federer's curvature measures''. Arch. Math. 46, 557–567 (1986).
https: / / doi.org/ 10.1007 / BF01195026

[61] David Cohen-Steiner and Jean-Marie Morvan. ``Restricted Delaunay triangulations and normal cycle''. In SCG '03: Proceedings of the nineteenth annual symposium on Computational geometry. Pages 312–321. (2003).
https: / / doi.org/ 10.1145 / 777792.777839

[62] Pierre Roussillon and Joan Alexis Glaunès. ``Surface matching using normal cycles''. In Frank Nielsen and Frédéric Barbaresco, editors, Geometric Science of Information. Pages 73–80. Cham (2017). Springer International Publishing.
https:/​/​doi.org/​10.1007/​978-3-319-68445-1_9

[63] Kehua Su, Na Lei, Wei Chen, Li Cui, Hang Si, Shikui Chen, and Xianfeng Gu. ``Curvature adaptive surface remeshing by sampling normal cycle''. Computer-Aided Design 111, 1–12 (2019).
https://​doi.org/​10.1016/​j.cad.2019.01.004

[64] David A. Cox, John Little, and Donal O'Shea. ``Ideals, varieties, and algorithms''. Undergraduate Texts in Mathematics. Springer Cham. (2015). Fourth edition.
https:/​/​doi.org/​10.1007/​978-3-319-16721-3

[65] Guido A. Raggio. ``A remark on Bell's inequality and decomposable normal states''. Lett. Math. Phys. 15, 27–29 (1988).
https: / / doi.org/ 10.1007 / BF00416568

[66] Marc-Olivier Renou, David Trillo, Mirjam Weilenmann, Thinh P. Le, Armin Tavakoli, Nicolas Gisin, Antonio Acín, and Miguel Navascués. ``Quantum theory based on real numbers can be experimentally falsified''. Nature 600, 625–629 (2021). arXiv:2101.10873.
https:/​/​doi.org/​10.1038/​s41586-021-04160-4
arXiv: 2101.10873

[67] Andrea Coladangelo, Koon Tong Goh, and Valerio Scarani. ``All pure bipartite entangled states can be self-tested''. Nature Commun. 8, 15485 (2017). arXiv:1611.08062.
https: / / doi.org/ 10.1038 / ncomms15485
arXiv: 1611.08062

[68] Charles H. Bennett and Gilles Brassard. ``Quantum cryptography: Public key distribution and coin tossing''. Theoret. Comp. Sci. 560, 7–11 (2014). arXiv:2003.06557.
https: / / doi.org/ 10.1016 / j.tcs.2014.05.025
arXiv: 2003.06557

[69] T. Franz, F. Furrer, and R. F. Werner. ``Extremal quantum correlations and cryptographic security''. Phys. Rev. Lett. 106, 250502 (2011). arXiv:1010.1131.
https: / / doi.org/ 10.1103 / ফিজিরভাইলেট .106.250502
arXiv: 1010.1131

[70] Jędrzej Kaniewski. ``Weak form of self-testing''. Phys. Rev. Research 2, 033420 (2020). arXiv:1910.00706.
https://​/​doi.org/​10.1103/​PhysRevResearch.2.033420
arXiv: 1910.00706

[71] C. H. Bennett, G. Brassard, C. Crepeau, and U. M. Maurer. ``Generalized privacy amplification''. IEEE Transactions on Information Theory 41, 1915–1923 (1995).
https: / / doi.org/ 10.1109 / 18.476316

[72] Pavel Sekatski, Jean-Daniel Bancal, Xavier Valcarce, Ernest Y.-Z. Tan, Renato Renner, and Nicolas Sangouard. ``Device-independent quantum key distribution from generalized CHSH inequalities''. Quantum 5, 444 (2021). arXiv:2009.01784.
https:/​/​doi.org/​10.22331/​q-2021-04-26-444
arXiv: 2009.01784

[73] Ernest Y.-Z. Tan, Pavel Sekatski, Jean-Daniel Bancal, René Schwonnek, Renato Renner, Nicolas Sangouard, and Charles C.-W. Lim. ``Improved DIQKD protocols with finite-size analysis''. Quantum 6, 880 (2022). arXiv:2012.08714.
https:/​/​doi.org/​10.22331/​q-2022-12-22-880
arXiv: 2012.08714

[74] Marissa Giustina et al. ``Significant-loophole-free test of Bell's theorem with entangled photons''. Phys. Rev. Lett. 115, 250401 (2015). arXiv:1511.03190.
https: / / doi.org/ 10.1103 / ফিজিরভাইলেট .115.250401
arXiv: 1511.03190

[75] Lynden K. Shalm et al. ``Strong loophole-free test of local realism''. Phys. Rev. Lett. 115, 250402 (2015). arXiv:1511.03189.
https: / / doi.org/ 10.1103 / ফিজিরভাইলেট .115.250402
arXiv: 1511.03189

[76] D. P Nadlinger, J.-D. Bancal, and et al. ``Experimental quantum key distribution certified by Bell's theorem''. Nature 607, 682–686 (2022). arXiv:2109.14600.
https:/​/​doi.org/​10.1038/​s41586-022-04941-5
arXiv: 2109.14600

[77] Wei Zhang, Harald Weinfurter, et al. ``A device-independent quantum key distribution system for distant users''. Nature 607, 687–691 (2022). arXiv:2110.00575.
https: / / doi.org/ 10.1038 / s41586-022-04891-y
arXiv: 2110.00575

[78] Feihu Xu, Yu-Zhe Zhang, Qiang Zhang, and Jian-Wei Pan. ``Device-independent quantum key distribution with random postselection''. Phys. Rev. Lett. 128, 110506 (2022). arXiv:2110.02701.
https: / / doi.org/ 10.1103 / ফিজিরভাইলেট .128.110506
arXiv: 2110.02701

[79] Wikipedia authors. ``Quantum key distribution''. url: https:/​/​en.wikipedia.org/​wiki/​Quantum_key_distribution. (accessed: 25-October-2021).
https://​/​en.wikipedia.org/​wiki/​Quantum_key_distribution

[80] Armin Tavakoli, Máté Farkas, Denis Rosset, Jean-Daniel Bancal, and Jedrzej Kaniewski. ``Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments''. Science Advances 7, eabc3847 (2021). arXiv:1912.03225.
https://​/​doi.org/​10.1126/​sciadv.abc3847
arXiv: 1912.03225

[81] Stephen J. Summers and Reinhard F. Werner. ``Maximal violation of Bell's inequalities for algebras of observables in tangent spacetime regions''. Ann. Inst. H. Poincaré. 49, 215–243 (1988).

[82] N. David Mermin. ``Is the moon there when nobody looks? Reality and the quantum theory''. Physics Today 38, 38–47 (1985).
https: / / doi.org/ 10.1063 / 1.880968

[83] Michael Janas, Michael E. Cuffaro, and Michel Janssen. ``Putting probabilities first. How Hilbert space generates and constrains them'' (2019) arXiv:1910.10688.
arXiv: 1910.10688

[84] Nicolas Brunner, Stefano Pironio, Antonio Acín, Nicolas Gisin, André Allan Méthot, and Valerio Scarani. ``Testing the dimension of Hilbert spaces''. Phys. Rev. Lett. 100, 210503 (2008). arXiv:0802.0760.
https: / / doi.org/ 10.1103 / ফিজিরভাইলেট .100.210503
arXiv: 0802.0760

[85] Yu Cai, Jean-Daniel Bancal, Jacquiline Romero, and Valerio Scarani. ``A new device-independent dimension witness and its experimental implementation''. J. Phys. A 49, 305301 (2016). arXiv:1606.01602.
https:/​/​doi.org/​10.1088/​1751-8113/​49/​30/​305301
arXiv: 1606.01602

[86] Wan Cong, Yu Cai, Jean-Daniel Bancal, and Valerio Scarani. ``Witnessing irreducible dimension''. Phys. Rev. Lett. 119, 080401 (2017). arXiv:1611.01258.
https: / / doi.org/ 10.1103 / ফিজিরভাইলেট .119.080401
arXiv: 1611.01258

[87] R. Horodecki, P. Horodecki, and M. Horodecki. ``Violating Bell inequality by mixed spin-1/​2 states: necessary and sufficient condition''. Phys. Lett. A 200, 340–344 (1995).
https:/​/​doi.org/​10.1016/​0375-9601(95)00214-N

[88] N. Gisin. ``Bell's inequality holds for all non-product states''. Physics Letters A 154, 201–202 (1991).
https:/​/​doi.org/​10.1016/​0375-9601(91)90805-I

[89] R. Grone, C.R. Johnson, E.M. Sá, and H. Wolkowicz. ``Positive definite completions of partial Hermitian matrices''. Lin. Alg. Appl. 58, 109–124 (1984).
https:/​/​doi.org/​10.1016/​0024-3795(84)90207-6

[90] Alexander Barvinok. ``A course in convexity''. Graduate Studies in Mathematics 54. AMS. Providence (2002).
https://​doi.org/​10.1090/​gsm/​054

[91] J. Dixmier. ``C*-algebras''. North-Holland mathematical library. North-Holland. (1982).

[92] M. Reed and B. Simon. ``Methods of modern mathematical physics IV: Analysis of operators''. Elsevier Science. (1978).

[93] Iain Raeburn and Allan M. Sinclair. ``The C*-algebra generated by two projections.''. Math. Scand. 65, 278–290 (1989).
https://​/​doi.org/​10.7146/​math.scand.a-12283

[94] Roy Araiza, Travis Russell, and Mark Tomforde. ``A universal representation for quantum commuting correlations''. Ann. Henri Poinc. 23, 4489–4520 (2022). arXiv:2102.05827.
https:/​/​doi.org/​10.1007/​s00023-022-01197-7
arXiv: 2102.05827

[95] I. Pitowsky. ``Quantum probability – quantum logic''. Volume 321 of Lect.Notes Phys. Springer. (1989).
https://​doi.org/​10.1007/​BFb0021186

[96] Dan Geiger, Christopher Meek, Bernd Sturmfels, et al. ``On the toric algebra of graphical models''. Ann. Statist. 34, 1463–1492 (2006). arXiv:math/​0608054.
https: / / doi.org/ 10.1214 / 009053606000000263
arXiv:math/0608054