Quantum probabilities as Bayesian probabilities

By Carlton M. Caves, Christopher A. Fuchs, Ruediger Schack. 2001

446 citations recorded by the source corpus.

In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper, we show that, despite being prescribed by a fundamental law, probabilities for individual quantum systems can be understood within the Bayesian approach. We argue that the distinction between classical and quantum probabilities lies not in their definition, but in the nature of the information they encode. In the classical world, maximal information about a physical system is complete in the sense of providing definite answers for all possible questions that can be asked of the system. In the quantum world, maximal information is not complete and cannot be completed. Using this distinction, we show that any Bayesian probability assignment in quantum mechanics must have the form of the quantum probability rule, that maximal information about a quantum system leads to a unique quantum-state assignment, and that quantum theory provides a stronger connection between probability and measured frequency than can be justified classically. Finally, we give a Bayesian formulation of quantum-state tomography.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/dfeb6521f5f2f8203de63de4eadd3b5583b96577

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Citations in the corpus

An introduction to QBism with an application to the locality of quantum mechanics (2013, background): “Since probabilities are the personal judgments of an agent, it follows that a quantum state assignment is also a personal judgment of the agent assigning that state.[13] The notorious “collapse of the wave-function” is nothing but the updating of an agent’s state assignment on the basis of her exper”
QBism, the Perimeter of Quantum Bayesianism (2010, background): “Solipsism on a stick, one might say.31 Quantum Bayesianism sidesteps the poisoned dart, as the previous sections have tried to convey, by asserting that quantum theory is just not a physical theory in the sense the accusers want it to be.”
Measurements on the reality of the wavefunction (2014, methodology): “Not all scientists—including in particular Quantum Bayesianists[2–4]—believe that our observations of the physical world can be entirely derived from an underlying objective reality.”
On Participatory Realism (2016, background): “John Archibald Wheeler’s writings were a tremendous influence on the point of view on quantum mechanics we now call QBism [1], developed by the author [2, 3, 4, 5] and colleagues Carlton Caves [6, 7, 8, 9], Asher Peres [10, 11], Marcus Appleby [12, 13, 14, 18, 15, 16, 17], Blake Stacey [19, 20, 21],”
Symmetric informationally complete–positive operator valued measures and the extended Clifford group (2004, unknown): “ar X iv :q ua nt -p h/ 04 12 00 1v 2 1 7 Ja n 20 05 SIC-POVMs AND THE EXTENDED CLIFFORD GROUP”
Quasi-probability representations of quantum theory with applications to quantum information science (2010, background): “Quantum Bayesianism (Caves et al 2002a, Fuchs 2002, Fuchs 2010, Fuchs and Schack 2009, Schack et al 2001) is an interpretation of quantum theory which sheds new light on not only the tradition ‘foundational’ problems (the ‘measurement problem’, for example) but also many concepts in quantum theory, ”
Evidence for the epistemic view of quantum states: A toy theory (2004, background): “This suggests that one would obtain a better analogy with quantum theory if states of complete knowledge were somehow impossible to achieve, that is, if somehow maximal knowledge was always incomplete knowledge [21, 22, 27].”