dorsal/arxiv
View SchemaUnknown Quantum States and Operations, a Bayesian View
| Authors | Christopher A. Fuchs, Ruediger Schack |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0404156 |
| URL | https://arxiv.org/abs/quant-ph/0404156 |
| DOI | 10.1007/b98673 |
Abstract
The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. In this paper, we motivate and review two results that generalize de Finetti's theorem to the quantum mechanical setting: Namely a de Finetti theorem for quantum states and a de Finetti theorem for quantum operations. The quantum-state theorem, in a closely analogous fashion to the original de Finetti theorem, deals with exchangeable density-operator assignments and provides an operational definition of the concept of an "unknown quantum state" in quantum-state tomography. Similarly, the quantum-operation theorem gives an operational definition of an "unknown quantum operation" in quantum-process tomography. These results are especially important for a Bayesian interpretation of quantum mechanics, where quantum states and (at least some) quantum operations are taken to be states of belief rather than states of nature.
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"abstract": "The classical de Finetti theorem provides an operational definition of the\nconcept of an unknown probability in Bayesian probability theory, where\nprobabilities are taken to be degrees of belief instead of objective states of\nnature. In this paper, we motivate and review two results that generalize de\nFinetti\u0027s theorem to the quantum mechanical setting: Namely a de Finetti\ntheorem for quantum states and a de Finetti theorem for quantum operations. The\nquantum-state theorem, in a closely analogous fashion to the original de\nFinetti theorem, deals with exchangeable density-operator assignments and\nprovides an operational definition of the concept of an \"unknown quantum state\"\nin quantum-state tomography. Similarly, the quantum-operation theorem gives an\noperational definition of an \"unknown quantum operation\" in quantum-process\ntomography. These results are especially important for a Bayesian\ninterpretation of quantum mechanics, where quantum states and (at least some)\nquantum operations are taken to be states of belief rather than states of\nnature.",
"arxiv_id": "quant-ph/0404156",
"authors": [
"Christopher A. Fuchs",
"Ruediger Schack"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/b98673",
"title": "Unknown Quantum States and Operations, a Bayesian View",
"url": "https://arxiv.org/abs/quant-ph/0404156"
},
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