dorsal/arxiv
View SchemaQuantum probabilities as Bayesian probabilities
| Authors | Carlton M. Caves, Christopher A. Fuchs, Ruediger Schack |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0106133 |
| URL | https://arxiv.org/abs/quant-ph/0106133 |
| DOI | 10.1103/PhysRevA.65.022305 |
| Journal | Phys. Rev. A 65, 022305 (2002) |
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.
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"abstract": "In the Bayesian approach to probability theory, probability quantifies a\ndegree of belief for a single trial, without any a priori connection to\nlimiting frequencies. In this paper we show that, despite being prescribed by a\nfundamental law, probabilities for individual quantum systems can be understood\nwithin the Bayesian approach. We argue that the distinction between classical\nand quantum probabilities lies not in their definition, but in the nature of\nthe information they encode. In the classical world, maximal information about\na physical system is complete in the sense of providing definite answers for\nall possible questions that can be asked of the system. In the quantum world,\nmaximal information is not complete and cannot be completed. Using this\ndistinction, we show that any Bayesian probability assignment in quantum\nmechanics must have the form of the quantum probability rule, that maximal\ninformation about a quantum system leads to a unique quantum-state assignment,\nand that quantum theory provides a stronger connection between probability and\nmeasured frequency than can be justified classically. Finally we give a\nBayesian formulation of quantum-state tomography.",
"arxiv_id": "quant-ph/0106133",
"authors": [
"Carlton M. Caves",
"Christopher A. Fuchs",
"Ruediger Schack"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.65.022305",
"journal_ref": "Phys. Rev. A 65, 022305 (2002)",
"title": "Quantum probabilities as Bayesian probabilities",
"url": "https://arxiv.org/abs/quant-ph/0106133"
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