Quantum Bayesianism

Quantum Bayesianism most often refers to a "subjective Bayesian account of quantum probability", that has evolved primarily from the work of Caves, Fuchs and Schack (published during 2002–2013), and draws from the fields of quantum information and Bayesian probability. It claims to correct, clarify, and extend the Copenhagen interpretation that is commonly taught in textbooks.

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" (Jaeger 2009) 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 (see also Störmer, 1969 ) 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.

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