Quantum probabilities as Bayesian probabilities Export

@misc{citeulike:680982, abstract = {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.}, archivePrefix = {arXiv}, author = {Caves, Carlton M. and Fuchs, Christopher A. and Schack, Ruediger}, citeulike-article-id = {680982}, citeulike-linkout-0 = {http://arxiv.org/abs/quant-ph/0106133}, citeulike-linkout-1 = {http://arxiv.org/pdf/quant-ph/0106133}, day = {14}, eprint = {quant-ph/0106133}, keywords = {bayes, bayesian, physics, probability, quantum, quantum-information}, month = {Nov}, posted-at = {2006-06-04 06:59:01}, priority = {2}, title = {Quantum probabilities as Bayesian probabilities}, url = {http://arxiv.org/abs/quant-ph/0106133}, year = {2001} }

TY - ELEC ID - citeulike:680982 L3 - citeulike-article-id:680982 N2 - 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. TI - Quantum probabilities as Bayesian probabilities KW - bayes KW - bayesian KW - physics KW - probability KW - quantum KW - quantum-information AU - Caves, Carlton AU - Fuchs, Christopher AU - Schack, Ruediger PY - 2001/Nov/14/ UR - http://arxiv.org/abs/quant-ph/0106133 ER -