Quantum-Bayesian coherence

Reviews of Modern Physics

Volumn 85, Issue 4, 2013, Pages

  Fuchs, Christopher A ^a,b   Schack, Rüdiger ^b,c  

^a PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

^b STELLENBOSCH UNIVERSITY   (South Africa)

^c UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

QUANTUM OPTICS;

BAYESIAN REASONING; CONDITIONAL PROBABILITIES; DUTCH BOOK; PHYSICAL SYSTEMS; PRIOR PROBABILITY; QUANTUM STATE; REFERENCE MEASUREMENTS; STATE SPACE STRUCTURES;

PROBABILITY;

EID: 84896934091     PISSN: 00346861     EISSN: 15390756     Source Type: Journal    
DOI: 10.1103/RevModPhys.85.1693     Document Type: Article

References (137)

1. Aczél, J., and Z. Daróczy, 1975, On Measures of Information and Their Characterizations, Mathematics in Science and Engineering Vol. 115 (Academic Press, New York).
2. Appleby, D.M., 2005 a, " SIC-POVMs and the Extended Clifford Group," J. Math. Phys. (N.Y.) 46, 052107. JMAPAQ 0022-2488 10.1063/1.1896384
3. Appleby, D.M., 2005 b, " Facts, Values and Quanta," Found. Phys. 35, 627. FNDPA4 0015-9018 10.1007/s10701-004-2014-6
4. Appleby, D.M., 2005 c, " Probabilities Are Single-Case, or Nothing," Opt. Spectrosc. 99, 447. OPSUA3 0030-400X 10.1134/1.2055942
5. Appleby, D.M., 2005 d, " The Bell-Kochen-Specker Theorem," Stud. Hist. Phil. Mod. Phys. 36, 1. 1355-2198 10.1016/j.shpsb.2004.05.003
6. Appleby, D.M., I. Bengtsson, S. Brierley, M. Grassl, D. Gross, and J.-A. Larsson, 2012, " The monomial representations of the Clifford group," Quantum Inf. Comput. 12, 404. QICUAW 1533-7146
7. Appleby, D.M., H.B. Dang, and C.A. Fuchs, 2007, " Symmetric Informationally-Complete Quantum States as Analogues to Orthonormal Bases and Minimum Uncertainty States," arXiv:0707.2071v2.
8. Appleby, D.M., Å. Ericsson, and C.A. Fuchs, 2011, " Properties of QBist State Spaces," Found. Phys. 41, 564. FNDPA4 0015-9018 10.1007/s10701-010-9458-7
9. Appleby, D.M., S.T. Flammia, and C.A. Fuchs, 2011, " The Lie Algebraic Significance of Symmetric Informationally Complete Measurements," J. Math. Phys. (N.Y.) 52, 022202. JMAPAQ 0022-2488 10.1063/1.3555805
10. Appleby, D.M., C.A. Fuchs, and Huangjun Zhu, 2013, unpublished.
11. Aspect, A., J. Dalibard, and G. Roger, 1982, " Experimental Test of Bell's Inequalities Using Time-Varying Analyzers," Phys. Rev. Lett. 49, 1804. PRLTAO 0031-9007 10.1103/PhysRevLett.49.1804
12. Baez, J., 2003, " Bayesian Probability Theory and Quantum Mechanics," http://math.ucr.edu/home/baez/bayes.html.
13. Ballentine, L.E., 1986, in New Techniques and Ideas in Quantum Measurement Theory, Annals of the New York Academy of Sciences Vol. 480, edited by, D.M. Greenberger, (New York Academy of Sciences, New York), pp. 382-392.
14. Barnum, H., J. Barrett, M. Leifer, and A. Wilce, 2006, " Cloning and Broadcasting in Generic Probabilistic Models," arXiv:quant-ph/0611295v1.
15. Barnum, H., C.M. Caves, C.A. Fuchs, R. Jozsa, and B. Schumacher, 1996, " Noncommuting Mixed States Cannot Be Broadcast," Phys. Rev. Lett. 76, 2818. PRLTAO 0031-9007 10.1103/PhysRevLett.76.2818
16. Barrett, J., and S. Pironio, 2005, " Popescu-Rohrlich Correlations as a Unit of Nonlocality," Phys. Rev. Lett. 95, 140401. PRLTAO 0031-9007 10.1103/PhysRevLett.95.140401
17. Bell, J., 1990, " Against 'Measurement'," Phys. World, August 1990, 33. PHWOEW 0953-8585
18. Bell, J.S., 1964, " On the Einstein Podolsky Rosen Paradox," Physics (Long Island City, N.Y.) 1, 195. PYCSAP 0554-128X
19. Bell, J.S., 1981, " Bertlmann's Socks and the Nature of Reality," J. Phys. (Paris), Colloq. 42, C2-41. JPQCAK 0449-1947 10.1051/jphyscol:1981202
20. Bell, J.S., 1987, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, England).
21. Bengtsson, I., and K. Życzkowski, 2006, Geometry of Quantum States: An Introduction to Quantum Entanglement (Cambridge University Press, Cambridge, England).
22. Bennett, C.H., G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W.K. Wootters, 1993, " Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels," Phys. Rev. Lett. 70, 1895. PRLTAO 0031-9007 10.1103/PhysRevLett.70.1895
23. Bennett, C.H., D.P. DiVincenzo, C.A. Fuchs, T. Mor, E. Rains, P.W. Shor, J.A. Smolin, and W.K. Wootters, 1999, " Quantum Nonlocality without Entanglement," Phys. Rev. A 59, 1070. PLRAAN 1050-2947 10.1103/PhysRevA.59. 1070
24. Bernardo, J.M., and A.F.M. Smith, 1994, Bayesian Theory (Wiley, Chichester).
25. Braunstein, S.L., S. Pirandola, and K. Życzkowski, 2013, " Better Late Than Never: Information Retrieval from Black Holes," Phys. Rev. Lett. 110, 101301. PRLTAO 0031-9007 10.1103/PhysRevLett.110.101301
26. Brun, T.A., J. Finkelstein, and N.D. Mermin, 2002, " How Much State Assignments Can Differ," Phys. Rev. A 65, 032315. PLRAAN 1050-2947 10.1103/PhysRevA.65.032315
27. Bub, J., 2011, in Probabilities in Physics, edited by, C. Beisbart, and, S. Hartmann, (Oxford University Press, Oxford).
28. Busch, P., M. Grabowski, and P.J. Lahti, 1995, Operational Quantum Mechanics (Springer, Berlin).
29. Busch, P., and P. Lahti, 2009, in Compendium of Quantum Physics, edited by, F. Weinert, K. Hentschel, and, D. Greenberger, (Springer-Verlag, Berlin), pp. 356-358.
30. Caticha, A., 2007, in Foundations of Probability and Physics-4, edited by, G. Adenier, C.A. Fuchs, and, A. Yu. Khrennikov, AIP Conf. Proc. No. 889 (AIP, Melville, NY).
31. Caves, C.M., 1999, " Symmetric Informationally Complete POVMs," http://info.phys.unm.edu/~caves/reports/infopovm.pdf.
32. Caves, C.M., 2002 (private communication).
33. Caves, C.M., and C.A. Fuchs, " Quantum Information: How Much Information in a State Vector?," 1996, Ann. Isr. Phys. Soc. 12, 226. AIPSDK 0309-8710
34. Caves, C.M., C.A. Fuchs, and R. Schack, 2002 a, " Unknown Quantum States: The Quantum de Finetti Representation," J. Math. Phys. (N.Y.) 43, 4537. JMAPAQ 0022-2488 10.1063/1.1494475
35. Caves, C.M., C.A. Fuchs, and R. Schack, 2002 b, " Conditions for Compatibility of Quantum-State Assignments," Phys. Rev. A 66, 062111. PLRAAN 1050-2947 10.1103/PhysRevA.66.062111
36. Caves, C.M., C.A. Fuchs, and R. Schack, 2007, " Subjective Probability and Quantum Certainty," Stud. Hist. Phil. Mod. Phys. 38, 255. 1355-2198 10.1016/j.shpsb.2006.10.007
37. Coffman, V., J. Kundu, and W.K. Wootters, 2000, " Distributed Entanglement," Phys. Rev. A 61, 052306. PLRAAN 1050-2947 10.1103/PhysRevA.61.052306
38. Cox, R.T., 1961, The Algebra of Probable Inference (Johns Hopkins Press, Baltimore).
39. D'Ariano, G.M., 2009, "Probabilistic Theories: What Is Special about Quantum Mechanics?," in Philosophy of Quantum Information and Entanglement, edited by, A. Bokulich, and, G. Jaeger, (Cambridge University Press, Cambridge, England).
40. de Finetti, B., 1931, " Probabilismo," Logos 14, 163 LGOSEL
41. [de Finetti, B. " Probabilism," Erkenntnis 31, 169 (1989)]. ERKEDQ
42. de Finetti, B., 1990, Theory of Probability (Wiley, New York), two volumes.
43. Demopoulos, W., 2010, " Effects and Propositions," Found. Phys. 40, 368. FNDPA4 0015-9018 10.1007/s10701-009-9321-x
44. Dennett, D.C., 2004, Freedom Evolves (Penguin Group, New York).
45. Diaconis, P., and S.L. Zabell, 1982, " Updating Personal Probability," J. Am. Stat. Assoc. 77, 822. JSTNAL 0162-1459 10.1080/01621459.1982.10477893
46. Dieks, D., 1982, " Communication by EPR devices," Phys. Lett. 92A, 271. PYLAAG 0375-9601 10.1016/0375-9601(82)90084-6
47. Einstein, A., 1951, in Albert Einstein: Philosopher-Scientist, edited by, P.A. Schilpp, (Tudor Co. Publishing, New York), pp. 81-87.
48. Ferrie, C., and J. Emerson, 2008, " Frame Representations of Quantum Mechanics and the Necessity of Negativity in Quasi-probability Representations," J. Phys. A 41, 352001. JPAMB5 1751-8113 10.1088/1751-8113/41/35/352001
49. Ferrie, C., and J. Emerson, 2009, " Framed Hilbert Space: Hanging the Quasi-probability Pictures of Quantum Theory," New J. Phys. 11, 063040. NJOPFM 1367-2630 10.1088/1367-2630/11/6/063040
50. Feynman, R.P., 1951, in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, edited by, J. Neyman, (University of California Press, Berkeley), pp. 533-541.
51. Feynman, R.P., R.B. Leighton, and M. Sands, 1965, The Feynman Lectures on Physics, Vol. 3 (Addison-Wesley, Reading, MA).
52. Flammia, S.T., 2004, unpublished.
53. Fuchs, C.A., 2002 a, " Quantum Mechanics as Quantum Information (and only a little more)," arXiv:quant-ph/0205039v1.
54. Fuchs, C.A., 2002 b, in Quantum Theory: Reconsideration of Foundations, edited by, A. Khrennikov, (Växjö University Press, Växjö, Sweden), pp. 99-116.
55. Fuchs, C.A., 2003, " Quantum Mechanics as Quantum Information, Mostly," J. Mod. Opt. 50, 987. JMOPEW 0950-0340
56. Fuchs, C.A., 2004, " On the Quantumness of a Hilbert Space," Quantum Inf. Comput. 4, 467. QICUAW 1533-7146
57. Fuchs, C.A., 2007, in Foundations of Probability and Physics-4, edited by, G. Adenier, C.A. Fuchs, and, A.Yu. Khrennikov, AIP Conf. Proc. Vol. 889 (American Institute of Physics, Melville, NY), pp. 438-462.
58. Fuchs, C.A., 2010 a, Coming of Age with Quantum Information (Cambridge University Press, Cambridge, England).
59. Fuchs, C.A., 2010 b, " QBism, the Perimeter of Quantum Bayesianism," arXiv:1003.5209v1.
60. Fuchs, C.A., 2012, " Interview with a Quantum Bayesian," arXiv:1207.2141v1.
61. Fuchs, C.A., 2013, My Struggles with the Block Universe, http://www.perimeterinstitute.ca/personal/cfuchs/.
62. Fuchs, C.A., and A. Peres, 2000, " Quantum Theory Needs No 'Interpretation'," Phys. Today 53, No. 3, 70. PHTOAD 0031-9228 10.1063/1.883004
63. Fuchs, C.A., and R. Schack, 2004, in Quantum Estimation Theory, edited by, M.G.A. Paris, and, J. Řeháček, (Springer-Verlag, Berlin), pp. 151-190.
64. Fuchs, C.A., and R. Schack, 2011, " A Quantum-Bayesian Route to Quantum-State Space," Found. Phys. 41, 345. FNDPA4 0015-9018 10.1007/s10701-009-9404-8
65. Fuchs, C.A., and R. Schack, 2012 a, in Probability in Physics, edited by, Y. Ben-Menahem, and, M. Hemmo, (Springer, Berlin), pp. 233-247.
66. Fuchs, C.A., and R. Schack, 2009, in Foundations of Probability and Physics-5, edited by, L. Accardi, AIP Conf. Proc. Vol. 1101 (American Institute of Physics, Melville, NY), pp. 255-259.
67. Gardner, M., 1983, The Whys of a Philosophical Scrivener (W. Morrow, New York).
68. Gieser, S., 2005, The Innermost Kernel: Depth Psychology and Quantum Physics. Wolfgang Pauli's Dialogue with C. G. Jung (Springer, Berlin).
69. Goyal, P., 2008, " An Information-Geometric Reconstruction of Quantum Theory, I: The Abstract Quantum Formalism," arXiv:0805.2761v1.
70. Grangier, P., 2002, " Contextual objectivity: a realistic interpretation of quantum mechanics," Eur. J. Phys. 23, 331. EJPHD4 0143-0807 10.1088/0143-0807/23/3/312
71. Grangier, P., 2005, " Contextual objectivity and the quantum formalism," Int. J. Quantum. Inform. 03, 17. 0219-7499 10.1142/ S0219749905000396
72. Hampton, J.M., P.G. Moore, and H. Thomas, 1973, " Probability and Its Measurement," J. R. Sta. Soc. A 136, 21. JSTAAG 0035-9238 10.2307/2344419
73. Hardy, L., 2001, " Quantum Theory From Five Reasonable Axioms," arXiv:quant-ph/0101012v4.
74. Holevo, A.S., 1982, Probabilistic and Statistical Aspects of Quantum Theory, North-Holland Series in Statistics and Probability Vol. 1 (North-Holland, Amsterdam).
75. Horn, R.A., and C.R. Johnson, 1985, Matrix Analysis (Cambridge University Press, Cambridge, England).
76. James, W., 1940, Some Problems of Philosophy: A Beginning of an Introduction to Philosophy (Longmans, Green, New York).
77. James, W., 1956 a, The Will to Believe, and Other Essays in Popular Philosophy (Dover, New York), pp. 263-298.
78. James, W., 1956 b, The Will to Believe, and Other Essays in Popular Philosophy (Dover, New York), pp. 145-183.
79. Jeffrey, R., 2004, Subjective Probability. The Real Thing (Cambridge University Press, Cambridge, England).
80. Jones, N.S., and N. Linden, 2005, " Parts of Quantum States," Phys. Rev. A 71, 012324. PLRAAN 1050-2947 10.1103/PhysRevA.71.012324
81. Kaznady, M.S., and D.F.V. James, 2009, " Numerical Strategies for Quantum Tomography: Alternatives to Full Optimization," Phys. Rev. A 79, 022109. PLRAAN 1050-2947 10.1103/PhysRevA.79.022109
82. Keynes, J.M., 1951, Essays in Biography (W. W. Norton, New York), pp. 243-244.
83. Koopman, B.O., 1957, in Proceedings of the Symposia in Applied Mathematics, Volume VII: Applied Probability, edited by, L.A. MacColl, (McGraw-Hill, New York), pp. 97-102.
84. Kyburg, Jr., H.E., and H.E. Smokler, 1980, Eds., Studies in Subjective Probability (Robert E. Krieger Publishing, Huntington, NY), 2nd ed.
85. Laurikainen, K.V., 1988, Beyond the Atom: The Philosophical Thought of Wolfgang Pauli (Springer-Verlag, Berlin).
86. Leifer, M.S., 2006, " Quantum Dynamics As an Analog of Conditional Probability," Phys. Rev. A 74, 042310. PLRAAN 1050-2947 10.1103/PhysRevA.74.042310
87. Leifer, M.S., 2007, in Foundations of Probability and Physics-4, AIP Conf. Proc. Vol. 889, edited by, G. Adenier, C.A. Fuchs, and, A.Yu. Khrennikov, (AIP, Melville, NY), pp. 172-186.
88. Leifer, M.S., and R.W. Spekkens, 2011, " Formulating Quantum Theory as a Causally Neutral Theory of Bayesian Inference," arXiv:1107.5849v3.
89. Lewis, D., 1986 a, Studies in Inductive Logic and Probability, Vol. II (Oxford University Press, Oxford), pp. 83-112.
90. Lewis, D., 1986 b, Philosophical Papers, Vol. II (Oxford University Press, Oxford), pp. 114-132.
91. Lindley, D.V., 1982, " Comment on A. P. Dawid's, 'The Well-Calibrated Bayesian'," J. Am. Stat. Assoc. 77, 611. JSTNAL 0162-1459
92. Lindley, D.V., 2006, Understanding Uncertainty (Wiley Interscience, Hoboken, NJ).
93. Mermin, N.D., 1993, " Hidden Variables and Two Theorems of John Bell," Rev. Mod. Phys. 65, 803. RMPHAT 0034-6861 10.1103/RevModPhys.65.803
94. Mermin, N.D., 1999, " Nonlocality and the absurd," Found. Phys. 29, 571. FNDPA4 0015-9018 10.1023/A:1018864225930
95. Mermin, N.D., 2006, " In Praise of Measurement," Quantum Inf. Process. 5, 239. QIPUAT 1570-0755 10.1007/s11128-006-0017-2
96. Mermin, N.D., 2012, " Quantum Mechanics: Fixing the Shifty Split," Phys. Today 65, No. 7, 8. PHTOAD 0031-9228 10.1063/PT.3.1618
97. Nagel, T., 1989, The View from Nowhere (Oxford University Press, Oxford, England).
98. Nielsen, M.A., and I.L. Chuang, 2000, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England).
99. Norsen, T., 2006, " Bell Locality and the Nonlocal Character of Nature," Found. Phys. Lett. 19, 633. FPLEET 0894-9875 10.1007/s10702-006- 1055-9
100. Parikh, M.K., and E. Verlinde, 2005, " Sitter Holography with a Finite Number of States," J. High Energy Phys. JHEPFG 1029-8479 01 054. 10.1088/1126-6708/2005/01/054
101. Paris, M.G.A., and J. Řeháček, 2004, Eds., Quantum Estimation Theory (Springer-Verlag, Berlin).
102. Patton, C.M., and J.A. Wheeler, 1975, in Quantum Gravity: An Oxford Symposium, edited by, C.J. Isham, R. Penrose, and, D.W. Sciama, (Clarendon Press, Oxford), pp. 538-605.
103. Pauli, W., 1994, Writings on Physics and Philosophy, edited by, C.P. Enz, and, K. von Meyenn, (Springer-Verlag, Berlin).
104. Peres, A., 1978, " Unperformed Experiments Have No Results," Am. J. Phys. 46, 745. AJPIAS 0002-9505 10.1119/1.11393
105. Peres, A., 1993, Quantum Theory: Concepts and Methods (Kluwer, Dordrecht).
106. Peres, A., 2005, " Einstein, Podolsky, Rosen, and Shannon," Found. Phys. 35, 511. FNDPA4 0015-9018 10.1007/s10701-004-1986-6
107. Pitowsky, I., 2003, " Betting on the Outcomes of Measurements: A Bayesian Theory of Quantum Probability," Stud. Hist. Phil. Mod. Phys. 34, 395. 1355-2198 10.1016/S1355-2198(03)00035-2
108. Pitowsky, I., 2005, " Quantum Mechanics as a Theory of Probability," arXiv:quant-ph/0510095v1.
109. Plotnitsky, A., 2006, Reading Bohr: Physics and Philosophy (Springer, Dordrecht).
110. Plunk, G.G., 2002, " Investigations on Informationally Complete Measurements," Bell Labs Summer Research Program, Summer (unpublished); see also Sec. VC of arXiv:1301.3274v1.
111. Popescu, S., and D. Rohrlich, 1994, " Quantum Nonlocality as an Axiom," Found. Phys. 24, 379. FNDPA4 0015-9018 10.1007/BF02058098
112. Porta Mana, P.G.L., 2007, Ph.D. thesis (KTH, Stockholm, Sweden).
113. Price, H., 1997, Time's Arrow & Archimedes' Point: New Directions for the Physics of Time (Oxford University Press, Oxford, England).
114. Ramsey, F.P., 1931, in The Foundations of Mathematics and other Logical Essays, edited by, R.B. Braithwaite, (Harcourt, Brace and Company, New York), pp. 156-198.
115. Rau, J., 2009, " On Quantum vs Classical Probability," Ann. Phys. (Amsterdam) 324, 2622. APNYA6 0003-4916 10.1016/j.aop.2009.09.013
116. Renes, J.M., R. Blume-Kohout, A.J. Scott, and C.M. Caves, 2004, " Symmetric Informationally Complete Quantum Measurements," J. Math. Phys. (N.Y.) 45, 2171. JMAPAQ 0022-2488 10.1063/1.1737053
117. Savage, L.J., 1954, The Foundations of Statistics (Wiley, New York).
118. Schack, R., 2003, " Quantum Theory from Four of Hardy's Axioms," Found. Phys. 33, 1461. FNDPA4 0015-9018 10.1023/A:1026044329659
119. Schack, R., T.A. Brun, and C.M. Caves, 2001, " Quantum Bayes Rule," Phys. Rev. A 64, 014305. PLRAAN 1050-2947 10.1103/PhysRevA.64.014305
120. Schnetter, E., 2013 (private communication).
121. Scott, A.J., and M. Grassl, 2010, " SIC-POVMs: A New Computer Study," J. Math. Phys. (N.Y.) 51, 042203. JMAPAQ 0022-2488 10.1063/1.3374022
122. Skyrms, B., 1987 a, in Scientific Inquiry in Philosophical Perspective, edited by, N. Rescher, (University of Pittsburgh Press, Pittsburg), pp. 225-242.
123. Skyrms, B., 1987 b, " Dynamic Coherence and Probability Kinematics," Philos. Sci. 54, 1. PHSCA6 0031-8248 10.1086/289350
124. Spekkens, R.W., 2005, " Contextuality for Preparations, Transformations, and Unsharp Measurements," Phys. Rev. A 71, 052108. PLRAAN 1050-2947 10.1103/PhysRevA.71.052108
125. Spekkens, R.W., 2007, " Evidence for the Epistemic View of Quantum States: A Toy Theory," Phys. Rev. A 75, 032110. PLRAAN 1050-2947 10.1103/PhysRevA.75.032110
126. Spekkens, R.W., 2008, " Negativity and Contextuality are Equivalent Notions of Nonclassicality," Phys. Rev. Lett. 101, 020401. PRLTAO 0031-9007 10.1103/PhysRevLett.101.020401
127. Srednicki, M., 2005, " Subjective and Objective Probabilities in Quantum Mechanics," Phys. Rev. A 71, 052107. PLRAAN 1050-2947 10.1103/PhysRevA.71.052107
128. Tabia, G.N.M., 2012, " Experimental Scheme for Qubit and Qutrit Symmetric Informationally Complete Positive Operator-Valued Measurements Using Multiport Devices," Phys. Rev. A 86, 062107. PLRAAN 1050-2947 10.1103/PhysRevA.86.062107
129. Timpson, C.J., 2008, " Quantum Bayesianism: A Study," Stud. Hist. Phil. Mod. Phys. 39, 579. 1355-2198 10.1016/j.shpsb.2008.03.006
130. Warmuth, M.K., and D. Kuzmin, 2009, " Bayesian Generalized Probability Calculus for Density Matrices," arXiv:0901.1273v1.
131. Wheeler, J.A., 1982, in Mind in Nature: Nobel Conference XVII, Gustavus Adolphus College, St. Peter, Minnesota, edited by, R.Q. Elvee, (Harper & Row, San Francisco, CA), pp. 1-23.
132. Wootters, W.K., and W.H. Zurek, 1982, " A Single Quantum Cannot Be Cloned," Nature (London) 299, 802. NATUAS 0028-0836 10.1038/299802a0
133. Youssef, S., 2001, " Physics with Exotic Probability Theory," arXiv:hep-th/0110253v2.
134. Zauner, G., 1999, " Quantum Designs-Foundations of a Non-Commutative Theory of Designs, Ph.D. thesis (University of Vienna) (in German).
135. Zeilinger, A., 1996, "On the Interpretation and Philosophical Foundation of Quantum Mechanics," in Vastakohtien todellisuus, Juhlakirja Professori K. V. Laurikaisen 80-vuotispäivänä, edited by, U. Ketvel, (Helsinki University Press, Helsinki), pp. 167-178.
136. Zinn-Justin, J., 2007, Phase Transitions and Renormalization Group (Oxford University Press, Oxford, England).
137. Zukowski, M., 2005, " On the Paradoxical Book of Bell," Stud. Hist. Phil. Mod. Phys. 36, 566. 1355-2198 10.1016/j.shpsb.2005.05.005