A Quantum-Bayesian Route to Quantum-State Space

By Christopher A. Fuchs, Ruediger Schack. 2009

154 citations recorded by the source corpus.

In the quantum-Bayesian approach to quantum foundations, a quantum state is viewed as an expression of an agent’s personalist Bayesian degrees of belief, or probabilities, concerning the results of measurements. These probabilities obey the usual probability rules as required by Dutch-book coherence, but quantum mechanics imposes additional constraints upon them. In this paper, we explore the question of deriving the structure of quantum-state space from a set of assumptions in the spirit of quantum Bayesianism. The starting point is the representation of quantum states induced by a symmetric informationally complete measurement or SIC. In this representation, the Born rule takes the form of a particularly simple modification of the law of total probability. We show how to derive key features of quantum-state space from (i) the requirement that the Born rule arises as a simple modification of the law of total probability and (ii) a limited number of additional assumptions of a strong Bayesian flavor.

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

View Paper: https://www.semanticscholar.org/paper/e34801397ec32d87a78ed229efe7a030a1bf3cef

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Citations in the corpus

On Participatory Realism (2016, background): “Johannes Kofler said recently to Rüdiger Schack, “I am convinced we are biological machines.””
Reformulating and Reconstructing Quantum Theory (2011, background): “In the past decade a number of papers have been written on the topic of reconstructing quantum theory [36, 15, 18, 73, 63, 64, 31, 17, 55, 33, 48, 29, 24, 13].”