|This article relies on references to primary sources. (April 2012)|
Quantum Bayesianism most often refers to a "subjective Bayesian account of quantum probability", that has evolved primarily from the work of Carlton M. Caves, Christopher Fuchs and Rüdiger Schack, and draws from the fields of quantum information and Bayesian probability. It may sometimes refer more generically to approaches to quantum theory that use a Bayesian or personalist (aka "subjective") probabilistic approach to the probabilities that appear in quantum theory. The approach associated with Caves, Fuchs, and Schack has been referred to as the Radical Bayesian interpretation. It attempts to provide an understanding of quantum mechanics and to derive modern quantum mechanics from informational considerations. The remainder of this article concerns primarily the Caves-Fuchs-Schack Bayesian approach to quantum theory.
Quantum Bayesianism deals with common questions in the interpretation of quantum mechanics about the nature of wavefunction superposition, non-locality, and entanglement. As the interpretation of quantum mechanics is important to philosophers of science, some compare the idea of degree of belief and its application in Quantum Bayesianism with the idea of anti-realism from philosophy of science.
Fuchs and Schack have referred to their current approach to the quantum Bayesian program as "QBism". On a technical level, QBism uses symmetric, informationally-complete, positive operator-valued measures (SIC-POVMs) to rewrite quantum states (either pure or mixed) as a set of probabilities defined over the outcomes of a "Bureau of Standards" measurement. That is, if one translates a density matrix into a probability distribution over the outcomes of a SIC-POVM experiment, one can reproduce all the statistical predictions (normally computed by using the Born rule) on the density matrix from the SIC-POVM probabilities instead. The Born rule then takes on the function of relating one valid probability distribution to another, rather than of deriving probabilities from something apparently more fundamental. QBist foundational research stimulated interest in SIC-POVMs, which now have applications in quantum theory outside of foundational studies. Likewise, a quantum version of the de Finetti theorem, introduced by Caves, Fuchs and Schack to provide a QBist understanding of the idea of an "unknown quantum state", has found application elsewhere, in topics like quantum key distribution and entanglement detection.
In the field of probability theory, there are different interpretations of probability and different forms of statistical inference which influence the conclusions that can be made from analysis of uncertain phenomena. The two dominant approaches to statistical inference include the frequentist approach (called frequentist inference) and the Bayesian approach (called Bayesian inference). The Bayesian approach upon which Quantum Bayesianism relies generally refers to a mode of statistical inference originating in, and greatly extending, the work of Thomas Bayes in statistics and probability.
Quantum Bayesianism tries to find a new understanding of quantum mechanics by applying Bayesian inference. Any new insights into quantum mechanics are beneficial, especially in light of the recent attempts to combine quantum mechanics and general relativity into a theory of quantum gravity and the interest in quantum computation. Quantum mechanics is thought to be derivable from the principles of quantum information.
In the book Lost Causes in and beyond Physics, Streater writes "[t]he ﬁrst quantum Bayesian was von Neumann. In Die mathematischen Grundlagen der Quantenmechanik, he describes the measurement process of say the spin polarization of an electron source ...".
Quantum Bayesianism applies the Bayesian approach to the fundamentals of quantum mechanics. The Bayesian approach is a mode of statistical inference. It introduces the concept of "degree of belief".
When the wavefunction of a system is written as a linear combination of the eigenstates of an observable such as position, the squared modulus of the coefficient of the eigenstate is the probability of obtaining the corresponding eigenvalue as the result of a measurement of that observable. Since this is probabilistic, this leads to the question of whether the universe is deterministic and how this is consistent with events being described probabilistically. Another idea which Quantum Bayesianism tries to address is whether quantum mechanical probabilities are objective or subjective, and the implications of the Born rule for either.
Quantum Bayesianism is an alternative to the (more) popular Copenhagen interpretation of quantum mechanics, which is built upon the idea of wavefunction collapse. The Copenhagen interpretation does not assume a specific interpretation of probability.
Other approaches to quantum mechanics are broadly related in that they also treat quantum states as expressions of information, knowledge, belief, or expectation. All these approaches - including QBism - can be termed "psi-epistemic", but they differ in what they consider quantum states to be information or expectations 'about', as well as in the technical features of the mathematics they employ.
QBism should be distinguished from other applications of Bayesian probability in quantum physics. For example, quantum computer science uses Bayesian networks, which find applications in "medical diagnosis, monitoring of processes, and genetics". (A Bayesian framework is also used for neural networks.) Bayesian inference has also been applied in quantum theory in terms of probability densities over quantum states, and MaxEnt methods have been used in similar ways.
- Bayes factor
- Bayesian inference
- Bayesian probability
- Credible intervals
- Degree of belief
- Minority interpretations of quantum mechanics
- Philosophy of science
- Probability interpretation
- Probability theory
- Quantum information
- Quantum probability
- Statistical inference
- Wavefunction collapse
- Stairs, Allen (2011). "A loose and separate certainty: Caves, Fuchs and Schack on quantum probability one" (pdf). Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics 42 (3): 158–166. doi:10.1016/j.shpsb.2011.02.001. Retrieved April 2012.
- Jaeger, Gregg (2009). "3.7. The radical Bayesian interpretation". Entanglement, information, and the interpretation of quantum mechanics (Online-Ausg. ed.). Berlin: Springer. pp. 170–179. ISBN 978-3-540-92127-1.
- Timpson, Christopher Gordon (2008). "Quantum Bayesianism: A study" (postscript). Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics 39 (3): 579–609. doi:10.1016/j.shpsb.2008.03.006. Retrieved April 2012.
- Mermin (2012a), Mermin (2012b)
- Fuchs and Schack (2011); Appleby, Ericsson and Fuchs (2011); Rosado (2011); Fuchs (2012)
- Fuchs and Schack (2011); Appleby, Ericsson and Fuchs (2011); Fuchs (2012)
- Scott (2006); Wootters and Sussman (2007); Fuchs (2012); Appleby et al. (2012)
- Caves, Fuchs and Schack (2002); Baez (2007)
- Renner (2005)
- Doherty et al. (2005)
- Streater. Lost Causes in and beyond Physics. Springer. p. 70. ISBN 3-540-36581-8.
- Talbott, William; Edward N. Zalta (Summer 2011 Edition). "Bayesian Epistemology". The Stanford Encyclopedia of Philosophy.
- Streater. Lost Causes in and beyond Physics. Springer. p. 69. ISBN 3-540-36581-8.
- Harrigan and Spekkens (2010)
- Bub and Pitowsky (2009)
- Marlow (2006); Smerlak and Rovelli (2007); Fuchs (2012)
- Fuchs and Schack (2013), footnote 3; Baez (2003).
- Tucci, Robert (17 Jun 1997). "Quantum Bayesian Nets". Int. Jour. Of Mod. Phys.
- MacKay, David (May 1992). "A Practical Bayesian Framework for Backpropagation Networks". Neural Computation 4: 448–472. doi:10.1162/neco.19188.8.131.528. Retrieved 30 April 2012.
- Jones (1991)
- Baez (2003), Canosa et al. (1992), Bužek et al. (1998).
- J. C. Baez (2003). "Bayesian Probability Theory and Quantum Mechanics".
- N. Canosa; R. Rossignoli; A. Plastino; H. G. Miller (1992). "Quantal entropy, fluctuations, and the description of many-body ground states". Physical Review C 45: 1162. doi:10.1103/PhysRevC.45.1162.
- K. R. W. Jones (1991). "Principles of quantum inference". Annals of Physics 207: 140. doi:10.1016/0003-4916(91)90182-8.
- Palge, Veiko; Konrad, Thomas (2008). "A remark on Fuchs’ Bayesian interpretation of quantum mechanics". Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics 39 (2): 273–287. doi:10.1016/j.shpsb.2007.10.002.
- Plotnitsky, Arkady (2010). Epistemology and probability : Bohr, Heisenberg, Schrödinger and the nature of quantum-theoretical thinking. New York: Springer. p. 12. ISBN 978-0-387-85333-8.
- C. M. Caves; C. A. Fuchs; R. Schack (2002). "Unknown quantum states: the quantum de Finetti representation". Journal of Mathematical Physics 43: 4537. arXiv:quant-ph/0104088. Bibcode:2002JMP....43.4537C. doi:10.1063/1.1494475.
- Renner, Renato (2005). "Security of Quantum Key Distribution (PhD thesis, ETH Zurich)". arXiv:quant-ph/0512258.
- A. C. Doherty; P. A. Parillo; F. M. Spedalieri (2005). "Detecting multipartite entanglement". Physical Review A 71 (3): 032333. arXiv:quant-ph/0407143. Bibcode:2005PhRvA..71c2333D. doi:10.1103/PhysRevA.71.032333.
- Marlow, Thomas (2006). "Relationalism vs. Bayesianism". arXiv:gr-qc/0603015.
- M. Smerlak; C. Rovelli (2007). "Relational EPR". Foundations of Physics 37: 427–445. arXiv:quant-ph/0604064. Bibcode:2007FoPh...37..427S. doi:10.1007/s10701-007-9105-0.
- A. J. Scott (2006). "Tight Informationally Complete Quantum Measurements". Journal of Physics A 39: 13507. arXiv:quant-ph/0604049. Bibcode:2006JPhA...3913507S. doi:10.1088/0305-4470/39/43/009.
- J. Baez (2007). "This Week's Finds in Mathematical Physics (Week 251)". Retrieved 29 April 2012.
- W. K. Wootters; D. M. Sussman (2007). Discrete phase space and minimum-uncertainty states. arXiv:0704.1277. Bibcode:2007arXiv0704.1277W.
- J. Bub; I. Pitowsky (2009). "Two dogmas about quantum mechanics". Everett @ 50. arXiv:0712.4258. Bibcode:2007arXiv0712.4258B.
- C. Brukner; A. Zeilinger (2009). "Information Invariance and Quantum Probabilities". Foundations of Physics 39: 677–689. arXiv:0905.0653. Bibcode:2009FoPh...39..677B. doi:10.1007/s10701-009-9316-7.
- Barnum, Howard (2010). "Quantum Knowledge, Quantum Belief, Quantum Reality: Notes of a QBist Fellow Traveler". arXiv:1003.4555.
- J. Bub (2010). "Quantum probabilities: an information-theoretic interpretation". Probabilities in Physics. arXiv:1005.2448. Bibcode:2010arXiv1005.2448B.
- N. Harrigan; R. Spekkens (2010). "Einstein, incompleteness, and the epistemic view of quantum states". Foundations of Physics 40: 125. arXiv:0706.2661. Bibcode:2010FoPh...40..125H. doi:10.1007/s10701-009-9347-0.
- Fuchs, C. A.; Schack, R. (2011). "A Quantum-Bayesian route to quantum-state space". Foundations of Physics 41 (3): 345–56. arXiv:0912.4252. Bibcode:2011FoPh...41..345F. doi:10.1007/s10701-009-9404-8.
- Appleby, D.M.; A. Ericsson; and C. A. Fuchs (2011). "Properties of QBist state spaces". Foundations of Physics 41 (3): 564–79. arXiv:0910.2750. Bibcode:2009arXiv0910.2750A.
- Appleby, D.M.; S. T. Flammia; and C. A. Fuchs (2011). "The Lie algebraic significance of symmetric informationally complete measurements". Journal of Mathematical Physics 52: 022202. arXiv:1001.0004. Bibcode:2010arXiv1001.0004A.
- J. I. Rosado (2011). "Representation of quantum states as points in a probability simplex associated to a SIC-POVM". Foundations of Physics 41 (3): 1200–13. arXiv:1007.0715. Bibcode:2011FoPh...41.1200R. doi:10.1007/s10701-011-9540-9.
- Leifer, M. S.; Spekkens, R. (2011). "Formulating Quantum Theory as a Causally Neutral Theory of Bayesian Inference". arXiv:1107.5849.
- Leifer, M. S.; Spekkens, R. (2011). "A Bayesian approach to compatibility, improvement, and pooling of quantum states". arXiv:1110.1085.
- Bartlett, S. D.; T. Rudolph; R. Spekkens (2011). "Reconstruction of Gaussian quantum mechanics from Liouville mechanics with an epistemic restriction". arXiv:1111.5057.
- Fuchs, Christopher (2011). Coming of Age with Quantum Information: Notes on a Paulian Idea. Cambridge University Press. ISBN 978-0-521-19926-1.
- X.-S. Ma et al. (2012). "Experimental delayed-choice entanglement swapping". Nature Physics. in press. arXiv:1203.4834. Bibcode:2012NatPh...8..480M. doi:10.1038/nphys2294.
- D.M. Appleby; I. Bengtsson; S. Brierley; M. Grassl; D. Gross; J.-A. Larsson (2012). "The monomial representations of the Clifford group". Quantum Information and Computation 12 (5&6): 0404–0431. arXiv:1102.1268. Bibcode:2011arXiv1102.1268A.
- C. A. Fuchs (27 April 2012). "My Struggles with the Block Universe". Retrieved 29 April 2012.
- Mermin, N. David. "Quantum mechanics: Fixing the shifty split". Physics Today 65 (7): 8. doi:10.1063/PT.3.1618.
- Mermin, N. David. "Measured responses to Quantum Bayesianism". Physics Today 65 (12): 12. doi:10.1063/PT.3.1803.
- von Baeyer, Hans Christian (2013). "Quantum Weirdness? It's all in your mind". Scientific American 308 (6): 6.
- C. A. Fuchs; R. Schack (2013). "Quantum-Bayesian coherence". Reviews of Modern Physics 85: 1693. doi:10.1103/RevModPhys.85.1693.
- V. Bužek; R. Derka; G. Adam; P.L. Knight (1998). "Reconstruction of Quantum States of Spin Systems: From Quantum Bayesian Inference to Quantum Tomography". Annals of Physics 266: 454. doi:10.1006/aphy.1998.5802.
von Baeyer, Hans Christian (2013). "Can Quantum Bayesianism Fix the Paradoxes of Quantum Mechanics?". Scientific American 2013 (June). Retrieved 6 June 2013.(subscription required)
- QBism, the Perimeter of Quantum Bayesianism
- That the World Can Be Shaped: Quantum Bayesianism, Counterfactuals, Free Will
- The Elegance of Enigma: Quantum Darwinism, Quantum Bayesianism (QBism) & Quantum Buddhism
- Quantum Mechanics as Quantum Information (and only a little more)
- Being Bayesian in a Quantum World - 2005 conference at the University of Konstanz
- Seeking SICs: A Workshop on Quantum Frames and Designs - 2008 conference at the Perimeter Institute