Quantum Bayesianism: A study

The Bayesian approach to quantum mechanics of Caves, Fuchs and Schack is presented. Its conjunction of realism about physics along with anti-realism about much of the structure of quantum theory is elaborated; and the position defended from common objections: that it is solipsist; that it is too instrumentalist; that it cannot deal with Wigner's friend scenarios. Three more substantive problems are raised: Can a reasonable ontology be found for the approach? Can it account for explanation in quantum theory? Are subjective probabilities on their own adequate in the quantum domain? The first question is answered in the affirmative, drawing on elements from Nancy Cartwright's philosophy of science. The second two are not: it is argued that these present outstanding difficulties for the project. A quantum Bayesian version of Moore's paradox is developed to illustrate difficulties with the subjectivist account of pure state assignments.

[1]  Philosophy of Quantum Information and Entanglement: Information, immaterialism, instrumentalism: Old and new in quantum information , 2010 .

[2]  Jane Heal,et al.  Moore's Paradox: A Wittgensteinian Approach , 1994 .

[3]  W. H. Zurek Complexity, Entropy and the Physics of Information , 1990 .

[4]  E. T. Jaynes,et al.  Papers on probability, statistics and statistical physics , 1983 .

[5]  W. Lamb Quantum Theory of Measurement , 1986 .

[6]  H. Barnum,et al.  Cloning and Broadcasting in Generic Probabilistic Theories , 2006, quant-ph/0611295.

[7]  Ron Dare,et al.  The disorder of things: Metaphysical foundations of the disunity of science , 1997 .

[8]  C. Fuchs Quantum Mechanics as Quantum Information (and only a little more) , 2002, quant-ph/0205039.

[9]  C. Fuchs,et al.  Quantum probabilities as Bayesian probabilities , 2001, quant-ph/0106133.

[10]  M. S. Leifer,et al.  Conditional Density Operators and the Subjectivity of Quantum Operations , 2006, quant-ph/0611233.

[11]  Patrick Suppes,et al.  Logic, Methodology and Philosophy of Science , 1963 .

[12]  N. Mermin Quantum theory: Concepts and methods , 1997 .

[13]  Carlton M. Caves,et al.  Subjective probability and quantum certainty , 2006 .

[14]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[15]  Csr Young,et al.  How to Do Things With Words , 2009 .

[16]  Christopher A. Fuchs,et al.  Quantum Foundations in the Light of Quantum Information , 2001 .

[17]  N. Bohr The Quantum Postulate and the Recent Development of Atomic Theory , 1928, Nature.

[18]  Andrei Khrennikov Quantum theory: Reconsideration of foundations , 2003 .

[19]  Amit Hagar,et al.  A Philosopher Looks at Quantum Information Theory* , 2003, Philosophy of Science.

[20]  Christopher G. Timpson,et al.  Philosophical Aspects of Quantum Information Theory 1 , 2007 .

[21]  E. Jaynes Information Theory and Statistical Mechanics , 1957 .

[22]  James B. Hartle,et al.  Quantum Mechanics of Individual Systems , 1968, 1907.02953.

[23]  A. Zeilinger A Foundational Principle for Quantum Mechanics , 1999, Synthese Library.

[24]  D. Greenberger,et al.  Whose knowledge? , 2001 .

[25]  Terence E Horgan,et al.  From Supervenience to Superdupervenience: Meeting the Demands of a Material World , 1993 .

[26]  Ruediger Schack,et al.  De Finetti representation theorem for quantum-process tomography (6 pages) , 2003, quant-ph/0307198.

[27]  H. Kyburg,et al.  How the laws of physics lie , 1984 .

[28]  Anjan Chakravartty,et al.  The Dappled World: A Study of the Boundaries of Science , 2000 .

[29]  C. Hoefer For Fundamentalism , 2003, Philosophy of Science.

[30]  William Band,et al.  The empirical determination of quantum states , 1970 .

[31]  Patrice E. A. Turchi,et al.  Decoherence and its implications in quantum computation and information transfer , 2001 .

[32]  J. Wheeler Information, physics, quantum: the search for links , 1999 .

[33]  Christopher A. Fuchs Delirium Quantum Or, where I will take quantum mechanics if it will let me , 2007 .

[34]  M. S. Leifer Quantum dynamics as an analog of conditional probability (12 pages) , 2006 .

[35]  A. Zeilinger,et al.  Speakable and Unspeakable in Quantum Mechanics , 1989 .

[36]  M. Redhead Quantum theory and measurement , 1984 .

[37]  Renato Renner,et al.  Security of quantum key distribution , 2005, Ausgezeichnete Informatikdissertationen.

[38]  H. Dingle The Laws of Nature* , 1944, Nature.

[39]  U. Fano Description of States in Quantum Mechanics by Density Matrix and Operator Techniques , 1957 .

[40]  E. Wigner Remarks on the Mind-Body Question , 1995 .

[41]  Jonathan Barrett Information processing in generalized probabilistic theories , 2005 .

[42]  T. Nagel The view from nowhere , 1987 .

[43]  C. Fuchs,et al.  Unknown Quantum States: The Quantum de Finetti Representation , 2001, quant-ph/0104088.

[44]  Niels Bohr,et al.  Discussion with Einstein on Epistemological Problems in Atomic Physics , 1996 .

[45]  C. Caves,et al.  Quantum Bayes rule , 2000, quant-ph/0008113.

[46]  R. Peierls In defence of “measurement” , 1991 .

[47]  N. David Mermin,et al.  Foundational, Historical, Anecdotal and Forward-Looking Thoughts on the Quantum , 2001 .

[48]  Asher Peres,et al.  Quantum Theory Needs No ‘Interpretation’ , 2000 .

[49]  Ruediger Schack,et al.  Unknown Quantum States and Operations, a Bayesian View , 2004, quant-ph/0404156.

[50]  Henry E. Kyburg,et al.  Studies in Subjective Probability , 1965 .

[51]  Jeffrey Bub,et al.  Quantum probabilities as degrees of belief , 2007 .

[52]  Peter Urbach,et al.  Scientific Reasoning: The Bayesian Approach , 1989 .

[53]  D. G. Rees,et al.  Foundations of Statistics , 1989 .

[54]  J. Bell,et al.  Speakable and Unspeakable in Quatum Mechanics , 1988 .

[55]  B. D. Finetti,et al.  Foresight: Its Logical Laws, Its Subjective Sources , 1992 .

[56]  A. Koller,et al.  Speech Acts: An Essay in the Philosophy of Language , 1969 .

[57]  Jeffrey Bub,et al.  Characterizing Quantum Theory in Terms of Information-Theoretic Constraints , 2002 .

[58]  N. Bohr II - Can Quantum-Mechanical Description of Physical Reality be Considered Complete? , 1935 .

[59]  G. Lindblad A General No-Cloning Theorem , 1999 .

[60]  R. Giere,et al.  Objective Single-Case Probabilities and the Foundations of Statistics , 1973 .

[61]  Lawrence B. Sklar Dappled Theories in a Uniform World* , 2003, Philosophy of Science.

[62]  Bruno de Finetti,et al.  Probabilism , 1989 .

[63]  M. Bredig,et al.  The Born-Einstein Letters , 1973, Science.

[64]  M. Born,et al.  Statistical Interpretation of Quantum Mechanics. , 1955, Science.

[65]  Christopher G Timpson,et al.  Philosophical Aspects of Quantum Information Theory , 2006, quant-ph/0611187.

[66]  C. Fuchs,et al.  Conditions for compatibility of quantum-state assignments , 2002, quant-ph/0206110.