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In a quantum-Bayesian take on quantum mechanics, the Born Rule cannot be interpreted as a rule for setting measurement-outcome probabilities from an objective quantum state.
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John Wheeler’s vision of quantum mechanics has been greatly inspiring to us, and overtones of his thought can be found throughout our own. The figure of his that suggested the present one can be found in several of Wheeler’s papers. See: C. M. Patton and J. A. Wheeler, “Is Physics Legislated by Cosmogony?,” in
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C. M. Caves and C. A. Fuchs, “Quantum Information: How Much Information in a State Vector?,” in
1996
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H. Price,
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G. Zauner,
1999
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C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, “Quantum Nonlocality without Entanglement,” Phys. Rev. A
1999
Cited alongside, same era.
For a few further suggestive things to read in this regard, we suggest: W. James,
1999
Cited alongside, same era.
D. Styer, S Sobottka, W. Holladay, T. A. Brun and R. B. Griffiths, P. Harris, letters to editor in “Quantum Theory—Interpretation, Formulation, Inspiration,” Phys. Tod
2000
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C. A. Fuchs and A. Peres, “Quantum Theory Needs No ‘Interpretation’,” Phys. Tod
2000
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V. Coffman, J. Kundu, and W. K. Wootters, “Distributed Entanglement,” Phys. Rev. A
2000
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A. Plotnitsky,
2006
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A. Hagar and M. Hemmo, “Explaining the Unobserved—Why Quantum Mechanics Ain’t Only About Information,” Found. Phys
2006
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A. Caticha, “From Objective Amplitudes to Bayesian Probabilities,”
2006
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M. S. Leifer, “Quantum Dynamics As an Analog of Conditional Probability,” Phys. Rev. A
2006
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M. S. Leifer, “Conditional Density Operators and the Subjectivity of Quantum Operations,” in
2006
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I. Bengtsson and K. Życzkowski,
2006
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M. Grassl, “Finding Equiangular Lines in Complex Space,” presentation at Magma 2006, Technische Universität Berlin, July 30 – August 2, 2006, posted at
2006
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A. J. Scott, “Tight Informationally Complete Quantum Measurements,” J. Phys. A
2006
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W. K. Wootters, “Quantum Measurements and Finite Geometry,” Found. Phys
2006
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S. T. Flammia, “On SIC-POVMs in Prime Dimensions,” J. Phys. A
2006
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I. H. Kim, “Quantumness, Generalized Spherical 2-Design and Symmetric Informationally Complete POVM,”
2006
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H. Barnum, J. Barrett, M. Leifer, and A. Wilce, “Cloning and Broadcasting in Generic Probabilistic Models,”
2006
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N. D. Mermin, “In Praise of Measurement,” Quant. Info. Process
2006
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D. V. Lindley,
2006
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C. M. Caves, C. A. Fuchs, and R. Schack, “Subjective Probability and Quantum Certainty,” Stud. Hist. Phil. Mod. Phys
2007
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U. Mohrhoff, “Objective Probability and Quantum Fuzziness,”
2007
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D. Wallace, “The Quantum Measurement Problem: State of Play,”
2007
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P. G. L. Porta Mana,
2007
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J. Rau, “On Quantum vs. Classical Probability,”
2007
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D. M. Appleby, H. B. Dang, and C. A. Fuchs, “Physical Significance of Symmetric Informationally-Complete Sets of Quantum States,”
2007
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D. M. Appleby, “Symmetric Informationally Complete Measurements of Arbitrary Rank,” Opt. Spectr
2007
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L. Bos and S. Waldron, “Some Remarks on Heisenberg Frames and Sets of Equiangular Lines,” New Zealand J. Math
2007
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O. Albouy and M. R. Kibler, “A Unified Approach to SIC-POVMs and MUBs,” J. Russ. Laser Res
2007
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P. Butterley and W. Hall, “Numerical Evidence for the Maximum Number of Mutually Unbiased Bases in Dimension Six,” Physics Letters A
2007
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R. W. Spekkens, “Evidence for the Epistemic View of Quantum States: A Toy Theory,” Phys. Rev. A
2007
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W. Demopoulos, “Effects and Propositions,”
2008
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V. Palge and T. Konrad, “A Remark on Fuchs’ Bayesian Interpretation of Quantum Mechanics,” Stud. Hist. Phil. Sci. Part B
2008
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2008
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C. J. Timpson,
2008
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C. H. Bennett, private communication, 8 July 2008
2008
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M. Grassl, private communication (2008)
2008
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M. Grassl, “Computing Equiangular Lines in Complex Space,”
2008
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M. Khatirinejad, “On Weyl-Heisenberg Orbits of Equiangular Lines,” J. Alg. Combin
2008
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C. Godsil and A. Roy, “Equiangular Lines, Mutually Unbiased Bases, and Spin Models,” Euro. J. Combin. (2008)
2008
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I. Bengtsson and H. Granström, “The Frame Potential, on Average,”
2008
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S. Brierley and S. Weigert, “Maximal Sets of Mutually Unbiased Quantum States in Dimension Six,” Phys. Rev. A
2008
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R. W. Spekkens, “Negativity and Contextuality are Equivalent Notions of Nonclassicality,” Phys. Rev. Lett
2008
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C. Ferrie and J. Emerson, “Frame Representations of Quantum Mechanics and the Necessity of Negativity in Quasi-probability Representations,” J. Phys. A
2008
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D. M. Appleby, private communication, 2008
2008
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G. M. D’Ariano, “Probabilistic Theories: What Is Special about Quantum Mechanics?,” in
2009
Closest in time.
M. K. Warmuth and D. Kuzmin, “Bayesian Generalized Probability Calculus for Density Matrices,”
2009
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C. A. Fuchs,
2009
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A. J. Scott, ongoing web-document “SIC-POVMs” (2009), posted at
2009
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S. Brierley and S. Weigert, “Constructing Mutually Unbiased Bases in Dimension Six,”
2009
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C. A. Fuchs and R. Schack, “Priors in Quantum Bayesian Inference,” in
2009
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M. S. Kaznady and D. F. V. James, “Numerical Strategies for Quantum Tomography: Alternatives to Full Optimization,” Phys. Rev. A
2009
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C. A. Fuchs, “Delirium Quantum: Or, where I will take quantum mechanics if it will let me,” in
2009
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W. Harper, S. J. Chow, and G. Murray, “Bayesian Chance,” to appear in Synthese (2009)
2009
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