PIRSA:11050023

Quantum Conditional States, Bayes Rule and Quantum Pooling

APA

Leifer, M. (2011). Quantum Conditional States, Bayes Rule and Quantum Pooling. Perimeter Institute for Theoretical Physics. https://pirsa.org/11050023

MLA

Leifer, Matthew. Quantum Conditional States, Bayes Rule and Quantum Pooling. Perimeter Institute for Theoretical Physics, May. 17, 2011, https://pirsa.org/11050023

BibTex

          @misc{ scivideos_PIRSA:11050023,
            doi = {10.48660/11050023},
            url = {https://pirsa.org/11050023},
            author = {Leifer, Matthew},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Quantum Conditional States, Bayes Rule and Quantum Pooling},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2011},
            month = {may},
            note = {PIRSA:11050023 see, \url{https://scivideos.org/pirsa/11050023}}
          }
          

Matthew Leifer Chapman University

Talk numberPIRSA:11050023
Source RepositoryPIRSA
Collection

Abstract

Quantum theory can be thought of a noncommutative generalization of classical probability and, from this perspective, it is puzzling that no quantum generalization of conditional probability is in widespread use. In this talk, I discuss one such generalization and show how it can unify the description of ensemble preparations of quantum states, POVM measurements and the description of correlations between quantum systems. The conditional states formalism allows for a description of prepare-and-measure experiments that is neutral with respect to the direction of inference, such that both the retrodictive formalism and the more usual predictive formalism are consequences of a more fundamental description in terms of a conditionally independent tripartite state, and the two formalisms are related by a quantum generalization of Bayes' rule. As an application, I give a generalized argument for the pooling rule proposed by Spekkens and Wiseman that is a direct analog of a result in classical supra-Bayesian pooling.