- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Reviews of Modern Physics

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Kochen-Specker contextuality

Costantino Budroni*, Adán Cabello, Otfried Gühne, Matthias Kleinmann, and Jan-Åke Larsson

Costantino Budroni*

  • Department of Physics “Enrico Fermi,” University of Pisa, Largo Bruno Pontecorvo 3, I-56127 Pisa, Italy, Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria, and Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria

Adán Cabello

  • Departamento de Física Aplicada II, Universidad de Sevilla, 41012 Sevilla, Spain and Instituto Carlos I de Física Teórica y Computacional, Universidad de Sevilla, 41012 Sevilla, Spain

Otfried Gühne and Matthias Kleinmann

  • Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany

Jan-Åke Larsson

  • Institutionen för Systemteknik och Matematiska Institutionen, Linköpings Universitet, 58183 Linköping, Sweden

  • *costantino.budroni@unipi.it
PDF

Rev. Mod. Phys. 94, 045007 – Published 19 December, 2022

DOI: https://doi.org/10.1103/RevModPhys.94.045007

Abstract

A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics is in conflict with classical models in which the result of a measurement does not depend on which other compatible measurements are jointly performed. Here compatible measurements are those that can be implemented simultaneously or, more generally, those that are jointly measurable. This conflict is generically called quantum contextuality. In this review, an introduction to this subject and its current status is presented. Several proofs of the Kochen-Specker theorem and different notions of contextuality are reviewed. How to experimentally test some of these notions is explained, and connections between contextuality and nonlocality or graph theory are discussed. Finally, some applications of contextuality in quantum information processing are reviewed.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (500)

  1. Aaronson, S., and D. Gottesman, 2004, Phys. Rev. A 70, 052328.
  2. Abbott, A. A., C. S. Calude, J. Conder, and K. Svozil, 2012, Phys. Rev. A 86, 062109.
  3. Abbott, A. A., C. S. Calude, M. J. Dinneen, and N. Huang, 2019, Phys. Scr. 94, 045103.
  4. Abbott, A. A., C. S. Calude, and K. Svozil, 2014, Math. Struct. Comput. Sci. 24, e240303.
  5. Abbott, A. A., C. S. Calude, and K. Svozil, 2015, J. Math. Phys. (N.Y.) 56, 102201.
  6. Abbott, A. A., C. Giarmatzi, F. Costa, and C. Branciard, 2016, Phys. Rev. A 94, 032131.
  7. Abramsky, S., R. S. Barbosa, M. Karvonen, and S. Mansfield, 2019, in Proceedings of the 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), Vancouver, British Columbia, Canada, 2019 (IEEE, New York), 10.1109/LICS.2019.8785677.
  8. Abramsky, S., R. S. Barbosa, K. Kishida, R. Lal, and S. Mansfield, 2015, in Proceedings of the 24th EACSL Annual Conference on Computer Science Logic (CSL 2015), Berlin, 2015, Leibniz International Proceedings in Informatics Vol. 41, edited by S. Kreutzer (Schloss Dagstuhl—Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany), pp. 211–228.
  9. Abramsky, S., R. S. Barbosa, and S. Mansfield, 2017, Phys. Rev. Lett. 119, 050504.
  10. Abramsky, S., and A. Brandenburger, 2011, New J. Phys. 13, 113036.
  11. Abramsky, S., S. Mansfield, and R. S. Barbosa, 2012, in Proceedings of the 8th International Workshop on Quantum Physics and Logic, Nijmegen, Netherlands, 2011, Vol. 95, edited by B. Jacobs, P. Selinger, and B. Spitters, pp. 1–14, 10.4204/EPTCS.95.
  12. Acín, A., N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, 2007, Phys. Rev. Lett. 98, 230501.
  13. Acín, A., T. Fritz, A. Leverrier, and A. B. Sainz, 2015, Commun. Math. Phys. 334, 533.
  14. Agüero Trejo, J. M., and C. S. Calude, 2021, Theor. Comput. Sci. 862, 3.
  15. Alda, V., 1980, Apl. Mat. 25, 373.
  16. Ali, S. T., C. Carmeli, T. Heinosaari, and A. Toigo, 2009, Found. Phys. 39, 593.
  17. Amaral, B., A. Cabello, M. Terra Cunha, and L. Aolita, 2018, Phys. Rev. Lett. 120, 130403.
  18. Amaral, B., and C. Duarte, 2019, Phys. Rev. A 100, 062103.
  19. Amaral, B., C. Duarte, and R. I. Oliveira, 2018, J. Math. Phys. (N.Y.) 59, 072202.
  20. Amaral, B., and M. Terra Cunha, 2018, On Graph Approaches to Contextuality and Their Role in Quantum Theory (Springer, New York).
  21. Amaral, B., M. Terra Cunha, and A. Cabello, 2014, Phys. Rev. A 89, 030101.
  22. Amaral, B., M. Terra Cunha, and A. Cabello, 2015, Phys. Rev. A 92, 062125.
  23. Ambainis, A., M. Banik, A. Chaturvedi, D. Kravchenko, and A. Rai, 2019, Quantum Inf. Process. 18, 111.
  24. Ambainis, A., A. Nayak, A. Ta-Shma, and U. Vazirani, 2002, J. ACM 49, 496.
  25. Amselem, E., M. Bourennane, C. Budroni, A. Cabello, O. Gühne, M. Kleinmann, J.-Å. Larsson, and M. Wieśniak, 2013, Phys. Rev. Lett. 110, 078901.
  26. Amselem, E., L. E. Danielsen, A. J. López-Tarrida, J. R. Portillo, M. Bourennane, and A. Cabello, 2012, Phys. Rev. Lett. 108, 200405.
  27. Amselem, E., M. Rådmark, M. Bourennane, and A. Cabello, 2009, Phys. Rev. Lett. 103, 160405.
  28. Anders, J., and D. E. Browne, 2009, Phys. Rev. Lett. 102, 050502.
  29. Anwer, H., N. Wilson, R. Silva, S. Muhammad, A. Tavakoli, and M. Bourennane, 2019, arXiv:1904.09766.
  30. Aolita, L., R. Gallego, A. Acín, A. Chiuri, G. Vallone, P. Mataloni, and A. Cabello, 2012, Phys. Rev. A 85, 032107.
  31. Appleby, D. M., 2000, arXiv:quant-ph/0005010.
  32. Appleby, D. M., 2001, arXiv:quant-ph/0109034.
  33. Appleby, D. M., 2002, Phys. Rev. A 65, 022105.
  34. Appleby, D. M., 2005, Stud. Hist. Philos. Sci. B 36, 1.
  35. Appleby, D. M., I. Bengtsson, and S. Chaturvedi, 2008, J. Math. Phys. (N.Y.) 49, 012102.
  36. Araújo, M., M. T. Quintino, C. Budroni, M. Terra Cunha, and A. Cabello, 2013, Phys. Rev. A 88, 022118.
  37. Aravind, P. K., 2004, Am. J. Phys. 72, 1303.
  38. Aravind, P. K., and F. Lee-Elkin, 1998, J. Phys. A 31, 9829.
  39. Arends, F., J. Ouaknine, and C. W. Wampler, 2011, in Graph-Theoretic Concepts in Computer Science, edited by P. Kolman and J. Kratochvíl (Springer, New York), pp. 23–34.
  40. Arias, M., G. Cañas, E. S. Gómez, J. F. Barra, G. B. Xavier, G. Lima, V. D’Ambrosio, F. Baccari, F. Sciarrino, and A. Cabello, 2015, Phys. Rev. A 92, 032126.
  41. Arkhipov, A., 2012, arXiv:1209.3819.
  42. Arvidsson-Shukur, D. R. M., N. Yunger Halpern, H. V. Lepage, A. A. Lasek, C. H. W. Barnes, and S. Lloyd, 2020, Nat. Commun. 11, 3775.
  43. Asadian, A., C. Budroni, F. E. S. Steinhoff, P. Rabl, and O. Gühne, 2015, Phys. Rev. Lett. 114, 250403.
  44. Aspect, A., J. Dalibard, and G. Roger, 1982, Phys. Rev. Lett. 49, 1804.
  45. Auffèves, A., and P. Grangier, 2020, Found. Phys. 50, 1781.
  46. Auffèves, A., and P. Grangier, 2022, Entropy 24, 199.
  47. Avis, D., 2018, http://cgm.cs.mcgill.ca/∼avis/C/lrs.html.
  48. Badziąg, P., I. Bengtsson, A. Cabello, and I. Pitowsky, 2009, Phys. Rev. Lett. 103, 050401.
  49. Ballentine, L., 2014, arXiv:1402.5689.
  50. Banik, M., S. S. Bhattacharya, S. K. Choudhary, A. Mukherjee, and A. Roy, 2014, Found. Phys. 44, 1230.
  51. Banik, M., S. S. Bhattacharya, A. Mukherjee, A. Roy, A. Ambainis, and A. Rai, 2015, Phys. Rev. A 92, 030103.
  52. Barbieri, M., C. Cinelli, P. Mataloni, and F. De Martini, 2005, Phys. Rev. A 72, 052110.
  53. Barbieri, M., G. Vallone, F. De Martini, and P. Mataloni, 2007, Opt. Spectrosc. 103, 129.
  54. Barnett, N., and J. P. Crutchfield, 2015, J. Stat. Phys. 161, 404.
  55. Barnett, S. M., and S. Croke, 2009, Adv. Opt. Photonics 1, 238.
  56. Barrett, J., L. Hardy, and A. Kent, 2005, Phys. Rev. Lett. 95, 010503.
  57. Barrett, J., and A. Kent, 2004, Stud. Hist. Philos. Sci. B 35, 151.
  58. Barrett, J., A. Kent, and S. Pironio, 2006, Phys. Rev. Lett. 97, 170409.
  59. Barrett, J., N. Linden, S. Massar, S. Pironio, S. Popescu, and D. Roberts, 2005, Phys. Rev. A 71, 022101.
  60. Bartosik, H., J. Klepp, C. Schmitzer, S. Sponar, A. Cabello, H. Rauch, and Y. Hasegawa, 2009, Phys. Rev. Lett. 103, 040403.
  61. Bassi, A., K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, 2013, Rev. Mod. Phys. 85, 471.
  62. Bechmann-Pasquinucci, H., and A. Peres, 2000, Phys. Rev. Lett. 85, 3313.
  63. Beer, K., and T. J. Osborne, 2018, Phys. Rev. A 98, 052124.
  64. Beeri, C., R. Fagin, D. Maier, and M. Yannakakis, 1983, J. ACM 30, 479.
  65. Belinfante, F. J., 1973, A Survey of Hidden-Variables Theories, 1st ed., International Series of Monographs in Natural Philosophy Vol. 55 (Pergamon Press, New York).
  66. Bell, J. S., 1964, Physics 1, 195.
  67. Bell, J. S., 1966, Rev. Mod. Phys. 38, 447.
  68. Bell, J. S., 1971, in Foundations of Quantum Mechanics, Proceedings of the International School of Physics “Enrico Fermi,” Course IL, edited by B. D’Espagnat (Academic Press, New York), pp. 171–181.
  69. Bell, J. S., 1982, Found. Phys. 12, 989.
  70. Beltrametti, E. G., and C. Cassinelli, 1981, The Logic of Quantum Mechanics (Addison-Wesley, Reading, MA).
  71. Bengtsson, I., 2009, AIP Conf. Proc. 1101, 241.
  72. Bengtsson, I., K. Blanchfield, and A. Cabello, 2012, Phys. Lett. A 376, 374.
  73. Bennett, C. H., and G. Brassard, 1984, in Proceedings of IEEE International Conference on Computers, Systems & Signal Processing, Bangalore, India, 1984 (IEEE, New York), pp. 175–179.
  74. Bermejo-Vega, J., N. Delfosse, D. E. Browne, C. Okay, and R. Raussendorf, 2017, Phys. Rev. Lett. 119, 120505.
  75. Bertlmann, R. A., and A. Zeilinger, 2013, Eds., Quantum (Un)speakables: From Bell to Quantum Information (Springer Science+Business Media, New York).
  76. Bharti, K., M. Ray, A. Varvitsiotis, A. Cabello, and L.-C. Kwek, 2019, arXiv:1911.09448.
  77. Bharti, K., M. Ray, A. Varvitsiotis, N. A. Warsi, A. Cabello, and L.-C. Kwek, 2019, Phys. Rev. Lett. 122, 250403.
  78. Bharti, K., M. Ray, Z.-P. Xu, M. Hayashi, L.-C. Kwek, and A. Cabello, 2021, arXiv:2104.13035.
  79. Birkhoff, G., and J. von Neumann, 1936, Ann. Math. 37, 823.
  80. Blasiak, P., 2015, Ann. Phys. (Amsterdam) 353, 326.
  81. Bohm, D., 1952a, Phys. Rev. 85, 166.
  82. Bohm, D., 1952b, Phys. Rev. 85, 180.
  83. Boole, G., 1862, Phil. Trans. R. Soc. London 152, 225.
  84. Borges, G., M. Carvalho, P.-L. de Assis, J. Ferraz, M. Araújo, A. Cabello, M. Terra Cunha, and S. Pádua, 2014, Phys. Rev. A 89, 052106.
  85. Born, M., 1926a, Z. Phys. 37, 863.
  86. Born, M., 1926b, Z. Phys. 38, 803.
  87. Boyd, S., and L. Vandenberghe, 2004, Convex Optimization (Cambridge University Press, Cambridge, England).
  88. Brassard, G., A. Broadbent, and A. Tapp, 2005, Found. Phys. 35, 1877.
  89. Braunstein, S. L., and C. M. Caves, 1988, Phys. Rev. Lett. 61, 662.
  90. Braunstein, S. L., and C. M. Caves, 1990, Ann. Phys. (N.Y.) 202, 22.
  91. Bravyi, S., D. Gosset, and R. König, 2018, Science 362, 308.
  92. Bravyi, S., D. Gosset, R. König, and M. Tomamichel, 2020, Nat. Phys. 16, 1040.
  93. Bravyi, S., and A. Kitaev, 2005, Phys. Rev. A 71, 022316.
  94. Bretto, A., 2013, Hypergraph Theory (Springer, Heidelberg).
  95. Briegel, H. J., D. E. Browne, W. Dür, R. Raussendorf, and M. Van den Nest, 2009, Nat. Phys. 5, 19.
  96. Brown, H. R., and G. Svetlichny, 1990, Found. Phys. 20, 1379.
  97. Brunner, N., D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, 2014, Rev. Mod. Phys. 86, 419.
  98. Bub, J., 1996, Found. Phys. 26, 787.
  99. Bub, J., 1997, Interpreting the Quantum World (Cambridge University Press, Cambridge, England).
  100. Budroni, C., and A. Cabello, 2012, J. Phys. A 45, 385304.
  101. Budroni, C., G. Fagundes, and M. Kleinmann, 2019, New J. Phys. 21, 093018.
  102. Budroni, C., N. Miklin, and R. Chaves, 2016, Phys. Rev. A 94, 042127.
  103. Budroni, C., and G. Morchio, 2010, J. Math. Phys. (N.Y.) 51, 122205.
  104. Budroni, C., G. Vitagliano, and M. P. Woods, 2021, Phys. Rev. Res. 3, 033051.
  105. Busch, P., P. Lahti, and R. F. Werner, 2014, Rev. Mod. Phys. 86, 1261.
  106. Busch, P., P. J. Lahti, and P. Mittelstaedt, 1996, The Quantum Theory of Measurement, 2nd ed., Lecture Notes in Physics Monographs Vol. 2 (Springer-Verlag, Berlin).
  107. Busch, P., P. J. Lahti, J.-P. Pellonpää, and K. Ylinen, 2016, Quantum Measurement, Theoretical and Mathematical Physics (Springer, New York).
  108. Cabello, A., 1994, Eur. J. Phys. 15, 179.
  109. Cabello, A., 1997, Phys. Rev. A 55, 4109.
  110. Cabello, A., 1999, arXiv:quant-ph/9911024.
  111. Cabello, A., 2001a, Phys. Rev. Lett. 87, 010403.
  112. Cabello, A., 2001b, Phys. Rev. Lett. 86, 1911.
  113. Cabello, A., 2002, Phys. Rev. A 65, 052101.
  114. Cabello, A., 2005, Phys. Rev. Lett. 95, 210401.
  115. Cabello, A., 2008, Phys. Rev. Lett. 101, 210401.
  116. Cabello, A., 2009, in Foundations of Probability and Physics, Vol. 5, edited by L. Accardi, G. Adenier, C. Fuchs, G. Jaeger, A. Y. Khrennikov, J.-Å. Larsson, and S. Stenholm (American Institute of Physics, New York), pp. 246–254.
  117. Cabello, A., 2010, Phys. Rev. Lett. 104, 220401.
  118. Cabello, A., 2011, arXiv:1112.5149.
  119. Cabello, A., 2012, arXiv:1212.1756.
  120. Cabello, A., 2013, Phys. Rev. Lett. 110, 060402.
  121. Cabello, A., 2015, Phys. Rev. Lett. 114, 220402.
  122. Cabello, A., 2016, Phys. Rev. A 93, 032102.
  123. Cabello, A., 2019a, Phil. Trans. R. Soc. A 377, 20190136.
  124. Cabello, A., 2019b, Phys. Rev. A 100, 032120.
  125. Cabello, A., 2021, Phys. Rev. Lett. 127, 070401.
  126. Cabello, A., E. Amselem, K. Blanchfield, M. Bourennane, and I. Bengtsson, 2012, Phys. Rev. A 85, 032108.
  127. Cabello, A., L. E. Danielsen, A. J. López-Tarrida, and J. R. Portillo, 2013, Phys. Rev. A 88, 032104.
  128. Cabello, A., J. M. Estebaranz, and G. García-Alcaine, 1996a, Phys. Lett. A 212, 183.
  129. Cabello, A., J. M. Estebaranz, and G. García-Alcaine, 1996b, Phys. Lett. A 218, 115.
  130. Cabello, A., J. M. Estebaranz, and G. García-Alcaine, 2005, Phys. Lett. A 339, 425.
  131. Cabello, A., and G. García-Alcaine, 1995, J. Phys. A 28, 3719.
  132. Cabello, A., and G. García-Alcaine, 1996, J. Phys. A 29, 1025.
  133. Cabello, A., and G. García-Alcaine, 1998, Phys. Rev. Lett. 80, 1797.
  134. Cabello, A., M. Gu, O. Gühne, J.-Å. Larsson, and K. Wiesner, 2016, Phys. Rev. A 94, 052127.
  135. Cabello, A., M. Gu, O. Gühne, and Z.-P. Xu, 2018, Phys. Rev. Lett. 120, 130401.
  136. Cabello, A., M. Kleinmann, and C. Budroni, 2015, Phys. Rev. Lett. 114, 250402.
  137. Cabello, A., M. Kleinmann, and J. R. Portillo, 2016, J. Phys. A 49, 38LT01.
  138. Cabello, A., and J.-Å. Larsson, 2010, Phys. Lett. A 375, 99.
  139. Cabello, A., J. R. Portillo, A. Solís, and K. Svozil, 2018, Phys. Rev. A 98, 012106.
  140. Cabello, A., S. Severini, and A. Winter, 2010, arXiv:1010.2163.
  141. Cabello, A., S. Severini, and A. Winter, 2014, Phys. Rev. Lett. 112, 040401.
  142. Carù, G., 2017, in Proceedings of the 13th International Workshop on Quantum Physics and Logic, Glasgow, Scotland, 2016, Vol. 236, edited by R. Duncan and C. Heunen, pp. 21–39, 10.4204/EPTCS.236.
  143. Cerf, N. J., N. Gisin, S. Massar, and S. Popescu, 2005, Phys. Rev. Lett. 94, 220403.
  144. Chailloux, A., I. Kerenidis, S. Kundu, and J. Sikora, 2016, New J. Phys. 18, 045003.
  145. Chaturvedi, A., M. Farkas, and V. J. Wright, 2020, arXiv:2010.05853.
  146. Chaves, R., 2013, Phys. Rev. A 87, 022102.
  147. Chaves, R., and T. Fritz, 2012, Phys. Rev. A 85, 032113.
  148. Chaves, R., L. Luft, and D. Gross, 2014, New J. Phys. 16, 043001.
  149. Chen, Z.-B., J.-W. Pan, Y.-D. Zhang, Č. Brukner, and A. Zeilinger, 2003, Phys. Rev. Lett. 90, 160408.
  150. Chernoff, P. R., 2009, Not. AMS 87, 1253, https://www.ams.org/notices/200910/rtx091001236p.pdf.
  151. Chiribella, G., A. Cabello, M. Kleinmann, and M. P. Müller, 2020, Phys. Rev. Res. 2, 042001.
  152. Chiribella, G., G. M. D’Ariano, and P. Perinotti, 2010, Phys. Rev. A 81, 062348.
  153. Chiribella, G., and X. Yuan, 2014, arXiv:1404.3348.
  154. Chiribella, G., and X. Yuan, 2016, Inf. Comput. 250, 15.
  155. Christof, T., and A. Loebel, 2015, http://porta.zib.de/.
  156. Cinelli, C., M. Barbieri, R. Perris, P. Mataloni, and F. De Martini, 2005, Phys. Rev. Lett. 95, 240405.
  157. Cirel’son, B. S., 1980, Lett. Math. Phys. 4, 93.
  158. Clauser, J. F., 1976a, Phys. Rev. Lett. 36, 1223.
  159. Clauser, J. F., 1976b, Nuovo Cimento Soc. Ital. Fis. 33B, 740.
  160. Clauser, J. F., M. A. Horne, A. Shimony, and R. A. Holt, 1969, Phys. Rev. Lett. 23, 880.
  161. Clauser, J. F., M. A. Horne, A. Shimony, and R. A. Holt, 1970, Phys. Rev. Lett. 24, 549(E).
  162. Cleve, R., P. Hoyer, B. Toner, and J. Watrous, 2004, in Proceedings of the 19th IEEE Annual Conference on Computational Complexity, Amherst, MA, 2004 (IEEE, New York), pp. 236–249.
  163. Clifton, R. K., 1993, Am. J. Phys. 61, 443.
  164. Clifton, R. K., and A. Kent, 2000, Proc. R. Soc. A 456, 2101.
  165. Coecke, B., T. Fritz, and R. W. Spekkens, 2016, Inf. Comput. 250, 59.
  166. Colbeck, R., 2006, Ph.D. thesis (University of Cambridge) [arXiv:0911.3814].
  167. Conway, J., and S. Kochen, 2006, Found. Phys. 36, 1441.
  168. Conway, J. H., and S. Kochen, 2009, Not. AMS 56, 226, https://www.ams.org/notices/200902/rtx090200226p.pdf.
  169. Conway, J. H., and S. Kochen, 2013, in Quantum (Un)speakables: From Bell to Quantum Information, edited by R. A. Bertlmann and A. Zeilinger (Springer Science+Business Media, New York), pp. 257–269.
  170. Correggi, M., and G. Morchio, 2002, Ann. Phys. (Amsterdam) 296, 371.
  171. Crutchfield, J. P., 1994, Physica (Amsterdam) 75D, 11.
  172. Cubitt, T. S., D. Leung, W. Matthews, and A. Winter, 2010, Phys. Rev. Lett. 104, 230503.
  173. Cubitt, T. S., D. Leung, W. Matthews, and A. Winter, 2011, IEEE Trans. Inf. Theory 57, 5509.
  174. Delfosse, N., P. Allard Guerin, J. Bian, and R. Raussendorf, 2015, Phys. Rev. X 5, 021003.
  175. Delfosse, N., C. Okay, J. Bermejo-Vega, D. E. Browne, and R. Raussendorf, 2017, New J. Phys. 19, 123024.
  176. de Obaldia, E., A. Shimony, and F. Wittel, 1988, Found. Phys. 18, 1013.
  177. De Simone, A., and P. Pták, 2015, Linear Algebra Appl. 481, 243.
  178. Diestel, R., 2018, Graph Theory (Springer, New York).
  179. Durucan, S., and A. Grinbaum, 2020, arXiv:2007.03450.
  180. Dvurečenskij, A., S. Pulmannová, and K. Svozil, 1995, Helv. Phys. Acta 68, 407.
  181. Einstein, A., B. Podolsky, and N. Rosen, 1935, Phys. Rev. 47, 777.
  182. Ekert, A. K., 1991, Phys. Rev. Lett. 67, 661.
  183. Elby, A., 1990a, Found. Phys. 20, 1389.
  184. Elby, A., 1990b, Found. Phys. Lett. 3, 239.
  185. Elby, A., and M. R. Jones, 1992, Phys. Lett. A 171, 11.
  186. Elitzur, A. C., S. Popescu, and D. Rohrlich, 1992, Phys. Lett. A 162, 25.
  187. Emary, C., N. Lambert, and F. Nori, 2014, Rep. Prog. Phys. 77, 016001.
  188. Emeriau, P.-E., M. Howard, and S. Mansfield, 2020, arXiv:2007.15643.
  189. Enz, C. P., B. Glaus, and G. Oberkofler, 1997, Wolfgang Pauli und Sein Wirken an der ETH Zürich (vdf Hochschulverlag AG an der ETH Zürich, Zürich).
  190. Fagundes, G., and M. Kleinmann, 2017, J. Phys. A 50, 325302.
  191. Fine, A., 1982a, Phys. Rev. Lett. 48, 291.
  192. Fine, A., 1982b, J. Math. Phys. (N.Y.) 23, 1306.
  193. Fine, A., 1990, Found. Phys. 20, 967.
  194. Foulis, D. J., and C. H. Randall, 1972, J. Math. Phys. (N.Y.) 13, 1667.
  195. Foulis, D. J., and C. H. Randall, 1974, Synthese 29, 81.
  196. Freedman, S. J., and J. F. Clauser, 1972, Phys. Rev. Lett. 28, 938.
  197. Frembs, M., S. Roberts, and S. D. Bartlett, 2018, New J. Phys. 20, 103011.
  198. Fritz, T., 2012, Rev. Math. Phys. 24, 1250012.
  199. Fritz, T., and R. Chaves, 2013, IEEE Trans. Inf. Theory 59, 803.
  200. Fritz, T., A. B. Sainz, R. Augusiak, J. B. Brask, R. Chaves, A. Leverrier, and A. Acín, 2013, Nat. Commun. 4, 2263.
  201. Froissart, M., 1981, Nuovo Cimento Soc. Ital. Fis. 64B, 241.
  202. Frustaglia, D., J. P. Baltanás, M. C. Velázquez-Ahumada, A. Fernández-Prieto, A. Lujambio, V. Losada, M. J. Freire, and A. Cabello, 2016, Phys. Rev. Lett. 116, 250404.
  203. Fuchs, C. A., 2002, arXiv:quant-ph/0205039.
  204. Fuchs, C. A., 2011, Coming of Age with Quantum Information: Notes on a Paulian Idea (Cambridge University Press, Cambridge, England).
  205. Fukuda, K., 2018, https://people.inf.ethz.ch/fukudak/cdd_home/.
  206. Galindo, A., 1975, in Algunas Cuestiones de Física Teórica (G.I.F.T., Zaragoza, Spain), pp. 3–9.
  207. Gao, X., E. R. Anschuetz, S.-T. Wang, J. I. Cirac, and M. D. Lukin, 2022, Phys. Rev. X 12, 021037.
  208. Garey, M. R., and D. S. Johnson, 2002, Computers and Intractability, Series of Books in the Mathematical Sciences Vol. 29 (W. H. Freeman, New York).
  209. Garg, A., and N. D. Mermin, 1984, Found. Phys. 14, 1.
  210. Gerelle, E. R., R. J. Greechie, and F. R. Miller, 1974, in Physical Reality & Mathematical Description, edited by C. P. Enz and J. Mehra (Reidel, Dordrecht), pp. 169–192.
  211. Ghorai, S., and A. K. Pan, 2018, Phys. Rev. A 98, 032110.
  212. Gibbons, K. S., M. J. Hoffman, and W. K. Wootters, 2004, Phys. Rev. A 70, 062101.
  213. Gill, R. D., and M. Keane, 1996, J. Phys. A 29, L289.
  214. Gleason, A. M., 1957, J. Math. Mech. 6, 885.
  215. Godsil, C. D., and J. Zaks, 1988, University of Waterloo Research Report No. CORR 88-12 [arXiv:1201.0486].
  216. Gottesman, D., 1997, Ph.D. thesis (California Institute of Technology) [arXiv:quant-ph/9705052].
  217. Gould, E., and P. K. Aravind, 2010, Found. Phys. 40, 1096.
  218. Grangier, P., 2021, Entropy 23, 1660.
  219. Greechie, R. J., 1971, J. Comb. Theory Ser. A 10, 119.
  220. Greenberger, D. M., M. A. Horne, and A. Zeilinger, 1989, in Bell’s Theorem, Quantum Theory and Conceptions of the Universe, Fundamental Theories of Physics Vol. 37, edited by M. Kafatos (Springer, New York), pp. 69–72.
  221. Griffiths, R. B., 2017, Phys. Rev. A 96, 032110.
  222. Griffiths, R. B., 2019, Phil. Trans. R. Soc. A 377, 20190033.
  223. Griffiths, R. B., 2020, Phys. Rev. A 101, 022117.
  224. Gross, D., 2006, J. Math. Phys. (N.Y.) 47, 122107.
  225. Grötschel, M., L. Lovász, and A. Schrijver, 1993, Geometric Algorithms and Combinatorial Optimization, Algorithms and Combinatorics Vol. 2 (Springer-Verlag, Berlin).
  226. Grudka, A., K. Horodecki, M. Horodecki, P. Horodecki, R. Horodecki, P. Joshi, W. Kłobus, and A. Wójcik, 2014, Phys. Rev. Lett. 112, 120401.
  227. Grünbaum, B., 2003, Convex Polytopes, 2nd ed. (Springer, New York).
  228. Gu, M., K. Wiesner, E. Rieper, and V. Vedral, 2012, Nat. Commun. 3, 762.
  229. Gühne, O., C. Budroni, A. Cabello, M. Kleinmann, and J.-Å. Larsson, 2014, Phys. Rev. A 89, 062107.
  230. Gühne, O., M. Kleinmann, A. Cabello, J.-Å. Larsson, G. Kirchmair, F. Zähringer, R. Gerritsma, and C. F. Roos, 2010, Phys. Rev. A 81, 022121.
  231. Hales, A. W., and E. G. Straus, 1982, Pac. J. Math. 99, 31.
  232. Hameedi, A., A. Tavakoli, B. Marques, and M. Bourennane, 2017, Phys. Rev. Lett. 119, 220402.
  233. Hardy, L., 1992, Phys. Rev. Lett. 68, 2981.
  234. Hardy, L., 1993, Phys. Rev. Lett. 71, 1665.
  235. Hardy, L., 2001, arXiv:quant-ph/0101012.
  236. Harrigan, N., and R. W. Spekkens, 2010, Found. Phys. 40, 125.
  237. Hasegawa, Y., R. Loidl, G. Badurek, M. Baron, and H. Rauch, 2003, Nature (London) 425, 45.
  238. Hasegawa, Y., R. Loidl, G. Badurek, M. Baron, and H. Rauch, 2006, Phys. Rev. Lett. 97, 230401.
  239. Hauge, E. H., and J. A. Støvneng, 1989, Rev. Mod. Phys. 61, 917.
  240. Havlicek, H., G. Krenn, J. Summhammer, and K. Svozil, 2001, J. Phys. A 34, 3071.
  241. Heinosaari, T., T. Miyadera, and M. Ziman, 2016, J. Phys. A 49, 123001.
  242. Heinosaari, T., and M. M. Wolf, 2010, J. Math. Phys. (N.Y.) 51, 092201.
  243. Heinosaari, T., and M. Ziman, 2012, The Mathematical Language of Quantum Theory: From Uncertainty to Entanglement (Cambridge University Press, Cambridge, England).
  244. Heisenberg, W., 1927, Z. Phys. 43, 172.
  245. Henson, J., 2012, arXiv:1210.5978.
  246. Henson, J., 2015, Phys. Rev. Lett. 114, 220403.
  247. Henson, J., and A. B. Sainz, 2015, Phys. Rev. A 91, 042114.
  248. Hermann, G., 1935, Abh. Fries’schen Sch. 6, 75.
  249. Herrmann, K., 2019, Grete Henry-Hermann: Philosophie—Mathematik—Quantenmechanik (Springer, New York).
  250. Heunen, C., T. Fritz, and M. L. Reyes, 2014, Phys. Rev. A 89, 032121.
  251. Heywood, P., and M. L. G. Redhead, 1983, Found. Phys. 13, 481.
  252. Hindlycke, C., and J.-Å. Larsson, 2022, Phys. Rev. Lett. 129, 130401.
  253. Hoban, M. J., E. T. Campbell, K. Loukopoulos, and D. E. Browne, 2011, New J. Phys. 13, 023014.
  254. Hoffmann, J., C. Spee, O. Gühne, and C. Budroni, 2018, New J. Phys. 20, 102001.
  255. Holevo, A. S., 1982, Probabilistic and Statistical Aspects of Quantum Theory (North-Holland, Amsterdam).
  256. Horn, A., and A. Tarski, 1948, Trans. Am. Math. Soc. 64, 467.
  257. Horodecki, K., A. Grudka, P. Joshi, W. K. lobus, and J. Lodyga, 2015, Phys. Rev. A 92, 032104.
  258. Horodecki, K., M. Horodecki, P. Horodecki, R. Horodecki, M. Pawlowski, and M. Bourennane, 2010, arXiv:1006.0468.
  259. Howard, M., J. Wallman, V. Veitch, and J. Emerson, 2014, Nature (London) 510, 351.
  260. Huang, Y.-F., C.-F. Li, Y.-S. Zhang, J.-W. Pan, and G.-C. Guo, 2003, Phys. Rev. Lett. 90, 250401.
  261. Jaeger, G., 2019, Phil. Trans. R. Soc. A 377, 20190025.
  262. Jerger, M., et al., 2016, Nat. Commun. 7, 12930.
  263. Johansson, N., and J.-Å. Larsson, 2017, Quantum Inf. Process. 16, 233.
  264. Johansson, N., and J.-Å. Larsson, 2019, Entropy 21, 800.
  265. Karvonen, M., 2021, Phys. Rev. Lett. 127, 160402.
  266. Karvonen, M., 2022 (private communication).
  267. Kellerer, H. G., 1964a, Math. Ann. 153, 168.
  268. Kellerer, H. G., 1964b, Z. Wahrscheinlichkeitstheorie verw. Gebiete 3, 247.
  269. Kent, A., 1999, Phys. Rev. Lett. 83, 3755.
  270. Kernaghan, M., 1994, J. Phys. A 27, L829.
  271. Kernaghan, M., and A. Peres, 1995, Phys. Lett. A 198, 1.
  272. Kirchmair, G., F. Zähringer, R. Gerritsma, M. Kleinmann, O. Gühne, A. Cabello, R. Blatt, and C. F. Roos, 2009, Nature (London) 460, 494.
  273. Kiukas, J., and R. F. Werner, 2010, J. Math. Phys. (N.Y.) 51, 072105.
  274. Kleinmann, M., 2014, J. Phys. A 47, 455304.
  275. Kleinmann, M., C. Budroni, J.-Å. Larsson, O. Gühne, and A. Cabello, 2012, Phys. Rev. Lett. 109, 250402.
  276. Kleinmann, M., O. Gühne, J. R. Portillo, J.-Å. Larsson, and A. Cabello, 2011, New J. Phys. 13, 113011.
  277. Klyachko, A. A., 2007, in Physics and Theoretical Computer Science: From Numbers and Languages to (Quantum) Cryptography, edited by J.-P. Gazeau, J. Nešetřil, and B. Rovan (IOP Press, London), pp. 25–54.
  278. Klyachko, A. A., M. A. Can, S. Binicioğlu, and A. S. Shumovsky, 2008, Phys. Rev. Lett. 101, 020403.
  279. Knuth, D. E., 1994, Electron. J. Comb. 1, A1.
  280. Kochen, S., 1970 (private communication).
  281. Kochen, S., and E. P. Specker, 1965a, in Proceedings of the International Congress for Logic, Methodology and Philosophy of Science, Jerusalem, 1964, edited by Y. Bar-Hillel (North-Holland, Amsterdam), pp. 45–57.
  282. Kochen, S., and E. P. Specker, 1965b, in Symposium on the Theory of Models: Proceedings of the 1963 International Symposium at Berkeley, edited by J. W. Addison, L. Henkin, and A. Tarski (North-Holland, Amsterdam), pp. 177–189.
  283. Kochen, S., and E. P. Specker, 1967, J. Math. Mech. 17, 59.
  284. Kofler, J., and Č. Brukner, 2013, Phys. Rev. A 87, 052115.
  285. Kong, X., M. Shi, F. Shi, P. Wang, P. Huang, Q. Zhang, C. Ju, C. Duan, S. Yu, and J. Du, 2012, arXiv:1210.0961.
  286. Kong, X., et al., 2016, arXiv:1602.02455.
  287. Krips, H., 1987, The Metaphysics of Quantum Theory (Clarendon Press, Oxford).
  288. Krishna, A., R. W. Spekkens, and E. Wolfe, 2017, New J. Phys. 19, 123031.
  289. Kujala, J. V., E. N. Dzhafarov, and J.-Å. Larsson, 2015, Phys. Rev. Lett. 115, 150401.
  290. Kulikov, A., M. Jerger, A. Potočnik, A. Wallraff, and A. Fedorov, 2017, Phys. Rev. Lett. 119, 240501.
  291. Kunjwal, R., 2015, Phys. Rev. A 91, 022108.
  292. Kunjwal, R., 2019, Quantum 3, 184.
  293. Kunjwal, R., 2020, Quantum 4, 219.
  294. Kunjwal, R., and S. Ghosh, 2014, Phys. Rev. A 89, 042118.
  295. Kunjwal, R., C. Heunen, and T. Fritz, 2014, Phys. Rev. A 89, 052126.
  296. Kunjwal, R., and R. W. Spekkens, 2015, Phys. Rev. Lett. 115, 110403.
  297. Kunjwal, R., and R. W. Spekkens, 2018, Phys. Rev. A 97, 052110.
  298. Kurzyński, P., R. Ramanathan, and D. Kaszlikowski, 2012, Phys. Rev. Lett. 109, 020404.
  299. La Cour, B. R., 2009, Phys. Rev. A 79, 012102.
  300. Landauer, R., and T. Martin, 1994, Rev. Mod. Phys. 66, 217.
  301. Łapkiewicz, R., P. Li, C. Schaeff, N. Langford, S. Ramelow, M. Wieśniak, and A. Zeilinger, 2011, Nature (London) 474, 490.
  302. Larsson, J.-Å., 2002, Europhys. Lett. 58, 799.
  303. Larsson, J.-Å., 2012, AIP Conf. Proc. 1424, 211.
  304. Larsson, J.-Å., 2014, J. Phys. A 47, 424003.
  305. Larsson, J.-Å., M. Kleinmann, O. Gühne, and A. Cabello, 2011, in Advances in Quantum Theory (Växjö, Sweden, 14–17 June 2010), edited by G. Jaeger, A. Y. Khrennikov, M. Schlosshauer, and G. Weihs (American Institute of Physics, New York), pp. 401–409.
  306. Lauritzen, S. L., 1996, Graphical Models (Clarendon Press, Oxford).
  307. Laversanne-Finot, A., A. Ketterer, M. R. Barros, S. P. Walborn, T. Coudreau, A. Keller, and P. Milman, 2017, J. Phys. A 50, 155304.
  308. Leggett, A. J., and A. Garg, 1985, Phys. Rev. Lett. 54, 857.
  309. Leifer, M., and C. Duarte, 2020, Phys. Rev. A 101, 062113.
  310. Leifer, M. S., and O. J. E. Maroney, 2013, Phys. Rev. Lett. 110, 120401.
  311. Leupold, F. M., M. Malinowski, C. Zhang, V. Negnevitsky, A. Cabello, J. Alonso, and J. P. Home, 2018, Phys. Rev. Lett. 120, 180401.
  312. Li, T., Q. Zeng, X. Song, and X. Zhang, 2017, Sci. Rep. 7, 44467.
  313. Liang, Y.-C., R. W. Spekkens, and H. M. Wiseman, 2011, Phys. Rep. 506, 1.
  314. Lisoněk, P., P. Badziąg, J. R. Portillo, and A. Cabello, 2014, Phys. Rev. A 89, 042101.
  315. Liu, B. H., Y. F. Huang, Y. X. Gong, F. W. Sun, Y. S. Zhang, C. F. Li, and G. C. Guo, 2009, Phys. Rev. A 80, 044101.
  316. Liu, B.-H., X.-M. Hu, J.-S. Chen, Y.-F. Huang, Y.-J. Han, C.-F. Li, G.-C. Guo, and A. Cabello, 2016, Phys. Rev. Lett. 117, 220402.
  317. Löhr, W., and N. Ay, 2009, in Proceedings of the First International Conference on Complex Sciences, Shanghai, 2009, edited by J. Zhou (Springer, New York), pp. 265–276.
  318. Lorentz, H. A., 1928, Électrons et Photons—Rapports et Discussions du Cinquième Conseil de Physique tenu à Bruxelles du 24 au 29 Octobre 1927 sous les Auspices de L’Institut International de Physique Solvay (Gauthier-Villars, Paris).
  319. Lörwald, S., and G. Reinelt, 2015, EURO J. Comput. Optim. 3, 297.
  320. Lostaglio, M., and G. Senno, 2020, Quantum 4, 258.
  321. Lovász, L., 1979, IEEE Trans. Inf. Theory 25, 1.
  322. Lovász, L., 2009, https://web.cs.elte.hu/~lovasz/geomrep.pdf.
  323. Lovejoy, A. O., 1936, The Great Chain of Being: A Study of the History of an Idea (Harvard University Press, Cambridge, MA).
  324. Ludwig, G., 1964, Z. Phys. 181, 233.
  325. Ludwig, G., 1967, Commun. Math. Phys. 4, 331.
  326. Ludwig, G., 1968, Commun. Math. Phys. 9, 1.
  327. Ludwig, G., 1972, Commun. Math. Phys. 26, 78.
  328. Lund, C., and M. Yannakakis, 1994, J. ACM 41, 960.
  329. Mackey, G. W., 1957, Am. Math. Mon. 64, 45.
  330. Mackey, G. W., 1963, Mathematical Foundations of Quantum Mechanics (Benjamin, New York).
  331. Malinowski, M., C. Zhang, F. M. Leupold, A. Cabello, J. Alonso, and J. P. Home, 2018, Phys. Rev. A 98, 050102.
  332. Malvestuto, F. M., 1988, Discrete Math. 69, 61.
  333. Mansfield, S., and E. Kashefi, 2018, Phys. Rev. Lett. 121, 230401.
  334. Mao, Y., C. Spee, Z.-P. Xu, and O. Gühne, 2020, arXiv:2005.13964.
  335. Mari, A., and J. Eisert, 2012, Phys. Rev. Lett. 109, 230503.
  336. Markiewicz, M., D. Kaszlikowski, P. Kurzyński, and A. Wójcik, 2019, npj Quantum Inf. 5, 5.
  337. Masanes, L., and M. P. Müller, 2011, New J. Phys. 13, 063001.
  338. Matsuno, S., 2007, J. Phys. A 40, 9507.
  339. Matúš, F., 2007a, Discrete Math. 307, 2464.
  340. Matúš, F., 2007b, in Proceedings of the IEEE International Symposium on Information Theory (ISIT 2007), Nice, France, 2007 (IEEE, New York), pp. 41–44.
  341. Mayers, D., and A. Yao, 2004, Quantum Inf. Comput. 4, 273.
  342. Mazurek, M. D., M. F. Pusey, R. Kunjwal, K. J. Resch, and R. W. Spekkens, 2016, Nat. Commun. 7, ncomms11780.
  343. Mealy, G. H., 1955, Bell Syst. Tech. J. 34, 1045.
  344. Megill, N. D., K. Fresl, M. Waegell, P. K. Aravind, and M. Pavičić, 2011, Phys. Lett. A 375, 3419.
  345. Meon, J., 1990, in Ernst Specker Selecta, edited by G. Jäger, H. Läuchli, B. Scarpellini, and V. Strassen (Birkhäuser Verlag, Basel), p. XI.
  346. Mermin, N. D., 1990a, Phys. Rev. Lett. 65, 1838.
  347. Mermin, N. D., 1990b, Phys. Rev. Lett. 65, 3373.
  348. Mermin, N. D., 1993, Rev. Mod. Phys. 65, 803.
  349. Mermin, N. D., 1999, arXiv:quant-ph/9912081.
  350. Mermin, N. D., and R. Schack, 2018, Found. Phys. 48, 1007.
  351. Meyer, D. A., 1999, Phys. Rev. Lett. 83, 3751.
  352. Michler, M., H. Weinfurter, and M. Żukowski, 2000, Phys. Rev. Lett. 84, 5457.
  353. Moussa, O., C. A. Ryan, D. G. Cory, and R. Laflamme, 2010, Phys. Rev. Lett. 104, 160501.
  354. Navascués, M., Y. Guryanova, M. J. Hoban, and A. Acín, 2015, Nat. Commun. 6, 6288.
  355. Navascués, M., S. Pironio, and A. Acín, 2007, Phys. Rev. Lett. 98, 010401.
  356. Navascués, M., S. Pironio, and A. Acín, 2008, New J. Phys. 10, 073013.
  357. Navascués, M., and H. Wunderlich, 2010, Proc. R. Soc. A 466, 881.
  358. Neumark, M. A., 1940a, Izv. Akad. Nauk SSSR, Ser. Mat. 4, 53, https://mathscinet.ams.org/mathscinet-getitem?mr=2713.
  359. Neumark, M. A., 1940b, Izv. Akad. Nauk SSSR, Ser. Mat. 4, 277, https://mathscinet.ams.org/mathscinet-getitem?mr=2714.
  360. Neumark, M. A., 1943, C.R. (Doklady) Acad. Sci. URSS 41, 359.
  361. Oestereich, A. L., and E. F. Galvão, 2017, Phys. Rev. A 96, 062305.
  362. Okay, C., and R. Raussendorf, 2020, Quantum 4, 217.
  363. Palsson, M. S., M. Gu, J. Ho, H. M. Wiseman, and G. J. Pryde, 2017, Sci. Adv. 3, e1601302.
  364. Pavičić, M., 2006, Quantum Computation and Quantum Communication: Theory and Experiments (Springer, New York).
  365. Pavičić, M., N. D. Megill, P. K. Aravind, and M. Waegell, 2011, J. Math. Phys. (N.Y.) 52, 022104.
  366. Pavičić, M., J.-P. Merlet, B. D. McKay, and N. D. Megill, 2005, J. Phys. A 38, 1577.
  367. Pawłowski, M., T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter, and M. Żukowski, 2009, Nature (London) 461, 1101.
  368. Penrose, R., 2000, in Quantum Reflections, edited by J. Ellis and D. Amati (Cambridge University Press, Cambridge, England), pp. 1–27.
  369. Peres, A., 1990, Phys. Lett. A 151, 107.
  370. Peres, A., 1991, J. Phys. A 24, L175.
  371. Peres, A., 1992, Found. Phys. 22, 357.
  372. Peres, A., 1993, Quantum Theory: Concepts and Methods (Kluwer, Dordrecht).
  373. Peres, A., 2003, arXiv:quant-ph/0310035.
  374. Peres, A., and A. Ron, 1988, in Microphysical Reality and Quantum Formalism, Vol. 2, edited by A. van der Merwe, F. Selleri, and G. Tarozzi (Kluwer, Dordrecht), pp. 115–123.
  375. Piron, C., 1964, Helv. Phys. Acta 37, 439.
  376. Piron, C., 1976, Foundations of Quantum Mechanics (W. A. Benjamin, Reading, MA).
  377. Pitowsky, I., 1985, Philos. Sci. 52, 154.
  378. Pitowsky, I., 1986, J. Math. Phys. (N.Y.) 27, 1556.
  379. Pitowsky, I., 1989, Quantum Probability—Quantum Logic, Lecture Notes in Physics Vol. 321 (Springer-Verlag, Berlin).
  380. Pitowsky, I., 1991, Math. Program. 50, 395.
  381. Pitowsky, I., 1994, Br. J. Philos. Sci. 45, 95.
  382. Planat, M., 2012, Eur. Phys. J. Plus 127, 86.
  383. Planat, M., 2013, in Symmetries and Groups in Contemporary Physics, edited by C. Bai, J.-P. Gazeau, and M.-L. Ge (World Scientific, Singapore), p. 295.
  384. Plastino, A. R., and A. Cabello, 2010, Phys. Rev. A 82, 022114.
  385. Popescu, S., and D. Rohrlich, 1994, Found. Phys. 24, 379.
  386. Pusey, M. F., 2018, Phys. Rev. A 98, 022112.
  387. Qu, D., P. Kurzyński, D. Kaszlikowski, S. Raeisi, L. Xiao, K. Wang, X. Zhan, and P. Xue, 2020, Phys. Rev. A 101, 060101.
  388. Rabelo, R., C. Duarte, A. J. López-Tarrida, M. Terra Cunha, and A. Cabello, 2014, J. Phys. A 47, 424021.
  389. Rabiner, L. R., 1989, Proc. IEEE 77, 257.
  390. Raeisi, S., P. Kurzyński, and D. Kaszlikowski, 2015, Phys. Rev. Lett. 114, 200401.
  391. Ramanathan, R., and P. Horodecki, 2014, Phys. Rev. Lett. 112, 040404.
  392. Ramanathan, R., A. Soeda, P. Kurzyński, and D. Kaszlikowski, 2012, Phys. Rev. Lett. 109, 050404.
  393. Randall, C. H., and D. J. Foulis, 1970, Am. Math. Mon. 77, 363.
  394. Randall, C. H., and D. J. Foulis, 1973, J. Math. Phys. (N.Y.) 14, 1472.
  395. Raussendorf, R., 2013, Phys. Rev. A 88, 022322.
  396. Raussendorf, R., 2019, Quantum Inf. Comput. 19, 1141.
  397. Raussendorf, R., and H. J. Briegel, 2001, Phys. Rev. Lett. 86, 5188.
  398. Raussendorf, R., D. E. Browne, N. Delfosse, C. Okay, and J. Bermejo-Vega, 2017, Phys. Rev. A 95, 052334.
  399. Ray, M., N. G. Boddu, K. Bharti, L.-C. Kwek, and A. Cabello, 2021, New J. Phys. 23, 033006.
  400. Redhead, M. L. G., 1987, Incompleteness, Nonlocality, and Realism (Oxford University Press, New York).
  401. Renner, R., and S. Wolf, 2004, in Proceedings of the International Symposium on Information Theory (ISIT 2004), Chicago, 2004 (IEEE, New York), p. 322.
  402. Ruuge, A. E., 2007, J. Phys. A 40, 2849.
  403. Ruuge, A. E., 2012, J. Phys. A 45, 465304.
  404. Sadiq, M., P. Badziag, M. Bourennane, and A. Cabello, 2013, Phys. Rev. A 87, 012128.
  405. Saha, D., and A. Chaturvedi, 2019, Phys. Rev. A 100, 022108.
  406. Saha, D., P. Horodecki, and M. Pawłowski, 2019, New J. Phys. 21, 093057.
  407. Saniga, M., and M. Planat, 2012, Quantum Inf. Comput. 12, 1011.
  408. Schaller, M., and K. Svozil, 1996, Int. J. Theor. Phys. 35, 911.
  409. Schmid, D., J. Selby, and R. W. Spekkens, 2020, arXiv:2009.03297.
  410. Schmid, D., J. Selby, E. Wolfe, R. Kunjwal, and R. W. Spekkens, 2021, PRX Quantum 2, 010331.
  411. Schmid, D., J. H. Selby, M. F. Pusey, and R. W. Spekkens, 2020, arXiv:2005.07161.
  412. Schmid, D., and R. W. Spekkens, 2018, Phys. Rev. X 8, 011015.
  413. Schmid, D., R. W. Spekkens, and E. Wolfe, 2018, Phys. Rev. A 97, 062103.
  414. Schrödinger, E., 1935, Proc. Cambridge Philos. Soc. 31, 555.
  415. Seevinck, M. P., 2011, arXiv:1103.4537.
  416. Selby, J. H., D. Schmid, E. Wolfe, A. B. Sainz, R. Kunjwal, and R. W. Spekkens, 2021, arXiv:2106.09045.
  417. Shannon, C., 1956, IRE Trans. Inf. Theory 2, 8.
  418. Shimony, A., 1971, in Foundations of Quantum Mechanics, Proceedings of the International School of Physics “Enrico Fermi,” Course IL, edited by B. D’Espagnat (Academic Press, New York), pp. 182–194.
  419. Shimony, A., 2009, in Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy, edited by D. Greenberger, K. Hentschel, and F. Weinert (Springer-Verlag, Berlin), pp. 287–291.
  420. Simon, C., Č. Brukner, and A. Zeilinger, 2001, Phys. Rev. Lett. 86, 4427.
  421. Soares Barbosa, R., 2014, Electron. Proc. Theor. Comput. Sci. 172, 36.
  422. Soares Barbosa, R., 2015, Ph.D. thesis (University of Oxford).
  423. Soares Barbosa, R., T. Douce, P.-E. Emeriau, E. Kashefi, and S. Mansfield, 2019, arXiv:1905.08267.
  424. Soares Barbosa, R., M. Karvonen, and S. Mansfield, 2021, arXiv:2104.11241.
  425. Specker, E., 1960, Dialectica 14, 239.
  426. Specker, E., 1999 (private communication).
  427. Spee, C., C. Budroni, and O. Gühne, 2020, New J. Phys. 22, 103037.
  428. Spekkens, R. W., 2005, Phys. Rev. A 71, 052108.
  429. Spekkens, R. W., 2007, Phys. Rev. A 75, 032110.
  430. Spekkens, R. W., 2014, Found. Phys. 44, 1125.
  431. Spekkens, R. W., 2019, arXiv:1909.04628.
  432. Spekkens, R. W., D. H. Buzacott, A. J. Keehn, B. Toner, and G. J. Pryde, 2009, Phys. Rev. Lett. 102, 010401.
  433. Stairs, A., 1978, Ph.D. thesis (University of Western Ontario).
  434. Stairs, A., 1983, Philos. Sci. 50, 578.
  435. Stomphorst, R. G., 2002, Phys. Lett. A 292, 213.
  436. Suppes, P., and M. Zanotti, 1981, Synthese 48, 191.
  437. Svozil, K., 2006, Am. J. Phys. 74, 800.
  438. Svozil, K., 2010, in Physics and Computation 2010, edited by H. Guerra (, Ponta Delgada, Portugal), pp. 235–249.
  439. Szangolies, J., 2015, Testing Quantum Contextuality: The Problem of Compatibility (Springer Spektrum, Wiesbaden).
  440. Szangolies, J., M. Kleinmann, and O. Gühne, 2013, Phys. Rev. A 87, 050101.
  441. Tavakoli, A., and R. Uola, 2020, Phys. Rev. Res. 2, 013011.
  442. Tavakoli, A., E. Zambrini Cruzeiro, R. Uola, and A. A. Abbott, 2021, PRX Quantum 2, 020334.
  443. Toh, S. P., 2013a, Chin. Phys. Lett. 30, 100302.
  444. Toh, S. P., 2013b, Chin. Phys. Lett. 30, 100303.
  445. Toner, B. F., and D. Bacon, 2003, Phys. Rev. Lett. 91, 187904.
  446. Trandafir, S., P. Lisoněk, and A. Cabello, 2022, arXiv:2202.13141.
  447. Tsirelson, B. S., 1993, Hadronic J. Suppl. 8, 329, https://www.tau.ac.il/~tsirel/download/hadron.pdf.
  448. Um, M., X. Zhang, J. Zhang, Y. Wang, Y. Shen, D.-L. Deng, L.-M. Duan, and K. Kim, 2013, Sci. Rep. 3, 1627.
  449. Um, M., Q. Zhao, J. Zhang, P. Wang, Y. Wang, M. Qiao, H. Zhou, X. Ma, and K. Kim, 2020, Phys. Rev. Appl. 13, 034077.
  450. Uola, R., A. C. S. Costa, H. C. Nguyen, and O. Gühne, 2020, Rev. Mod. Phys. 92, 015001.
  451. Uola, R., G. Vitagliano, and C. Budroni, 2019, Phys. Rev. A 100, 042117.
  452. van Dam, S. B., J. Cramer, T. H. Taminiau, and R. Hanson, 2019, Phys. Rev. Lett. 123, 050401.
  453. van Dam, W., 1999, Ph.D. thesis (University of Oxford), Chap. 9.
  454. van Enk, S. J., 2007, Found. Phys. 37, 1447.
  455. Veitch, V., C. Ferrie, D. Gross, and J. Emerson, 2012, New J. Phys. 14, 113011.
  456. Veitch, V., S. A. H. Mousavian, D. Gottesman, and J. Emerson, 2014, New J. Phys. 16, 013009.
  457. Vieira, L. B., and C. Budroni, 2022, Quantum 6, 623.
  458. von Neumann, J., 1931, Ann. Math. 32, 191.
  459. von Neumann, J., 1932, Mathematische Grundlagen der Quantenmechanik (Springer-Verlag, Berlin).
  460. Vorob’ev, N., 1962, Theory Probab. Appl. 7, 147.
  461. Vorob’ev, N., 1963, Theory Probab. Appl. 8, 420.
  462. Vorob’ev, N. N., 1959, Dokl. Akad. Nauk SSSR 124, 253.
  463. Vorob’yev, N. N., 1967, Theory Probab. Appl. 12, 251.
  464. Vourdas, A., 2004, Rep. Prog. Phys. 67, 267.
  465. Waegell, M., 2014, Phys. Rev. A 89, 012321.
  466. Waegell, M., and P. K. Aravind, 2010, J. Phys. A 43, 105304.
  467. Waegell, M., and P. K. Aravind, 2011a, J. Phys. A 44, 505303.
  468. Waegell, M., and P. K. Aravind, 2011b, Found. Phys. 41, 1786.
  469. Waegell, M., and P. K. Aravind, 2012, J. Phys. A 45, 405301.
  470. Waegell, M., and P. K. Aravind, 2013a, Phys. Lett. A 377, 546.
  471. Waegell, M., and P. K. Aravind, 2013b, Phys. Rev. A 88, 012102.
  472. Waegell, M., and P. K. Aravind, 2015, J. Phys. A 48, 225301.
  473. Waegell, M., and P. K. Aravind, 2017, Phys. Rev. A 95, 050101.
  474. Waegell, M., P. K. Aravind, N. D. Megill, and M. Pavičić, 2011, Found. Phys. 41, 883.
  475. Wang, P., J. Zhang, C.-Y. Luan, M. Um, Y. Wang, M. Qiao, T. Xie, J.-N. Zhang, A. Cabello, and K. Kim, 2022, Sci. Adv. 8, eabk1660.
  476. Wigner, E., 1932, Phys. Rev. 40, 749.
  477. Wilde, M. M., and A. Mizel, 2012, Found. Phys. 42, 256.
  478. Winter, A., 2014, J. Phys. A 47, 424031.
  479. Wiseman, H. M., S. J. Jones, and A. C. Doherty, 2007, Phys. Rev. Lett. 98, 140402.
  480. Wright, R., 1978, in Mathematical Foundations of Quantum Theory, edited by A. R. Marlow (Academic Press, New York), pp. 255–274.
  481. Xu, Z.-P., and A. Cabello, 2017, Phys. Rev. A 96, 012122.
  482. Xu, Z.-P., and A. Cabello, 2019, Phys. Rev. A 99, 020103.
  483. Xu, Z.-P., J.-L. Chen, and O. Gühne, 2020, Phys. Rev. Lett. 124, 230401.
  484. Xu, Z.-P., J.-L. Chen, and H.-Y. Su, 2015, Phys. Lett. A 379, 1868.
  485. Xu, Z.-P., D. Saha, H.-Y. Su, M. Pawłowski, and J.-L. Chen, 2016, Phys. Rev. A 94, 062103.
  486. Xu, Z.-P., X.-D. Yu, and M. Kleinmann, 2021, New J. Phys. 23, 043025.
  487. Yan, B., 2013, Phys. Rev. Lett. 110, 260406.
  488. Yang, T., Q. Zhang, J. Zhang, J. Yin, Z. Zhao, M. Żukowski, Z.-B. Chen, and J.-W. Pan, 2005, Phys. Rev. Lett. 95, 240406.
  489. Yeung, R. W., 2008, Information Theory and Network Coding, Information Technology—Transmission, Processing, and Storage (Springer, New York).
  490. Yu, S., and C. H. Oh, 2012, Phys. Rev. Lett. 108, 030402.
  491. Yu, X.-D., Y.-Q. Guo, and D. M. Tong, 2015, New J. Phys. 17, 093001.
  492. Yu, X.-D., and D. M. Tong, 2014, Phys. Rev. A 89, 010101.
  493. Zhan, X., E. G. Cavalcanti, J. Li, Z. Bian, Y. Zhang, H. M. Wiseman, and P. Xue, 2017, Optica 4, 966.
  494. Zhang, A., H. Xu, J. Xie, H. Zhang, B. J. Smith, M. S. Kim, and L. Zhang, 2019, Phys. Rev. Lett. 122, 080401.
  495. Zhang, X., M. Um, J. Zhang, S. An, Y. Wang, D.-l. Deng, C. Shen, L.-M. Duan, and K. Kim, 2013, Phys. Rev. Lett. 110, 070401.
  496. Zhang, Z., 2003, Commun. Inf. Syst. 3, 47.
  497. Zimba, J. R., and R. Penrose, 1993, Stud. Hist. Philos. Sci. A 24, 697.
  498. Zu, C., Y.-X. Wang, D.-L. Deng, X.-Y. Chang, K. Liu, P.-Y. Hou, H.-X. Yang, and L.-M. Duan, 2012, Phys. Rev. Lett. 109, 150401.
  499. Zu, C., Y.-X. Wang, D.-L. Deng, X.-Y. Chang, K. Liu, P.-Y. Hou, H.-X. Yang, and L.-M. Duan, 2013, Phys. Rev. Lett. 110, 078902.
  500. Zurel, M., C. Okay, and R. Raussendorf, 2020, Phys. Rev. Lett. 125, 260404.

Outline

Information

Rev. Mod. Phys. 94, 045007– Published 19 December, 2022
  • Received 12 March 2021
Crossmark - Check for updates button

© 2022 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation