dorsal/arxiv
View SchemaQuantum Dynamics as an analog of Conditional Probability
| Authors | M. S. Leifer |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0606022 |
| URL | https://arxiv.org/abs/quant-ph/0606022 |
| DOI | 10.1103/PhysRevA.74.042310 |
| Journal | Phys. Rev. A 74, 042310 (2006) |
Abstract
Quantum theory can be regarded as a non-commutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the well-known isomorphism between completely positive maps and bipartite density operators is derived, which makes this connection much more explicit. The new isomorphism is given an operational interpretation in terms of statistical correlations between ensemble preparation procedures and outcomes of measurements. Finally, the isomorphism is applied to elucidate the connection between no-cloning/no-broadcasting theorems and the monogamy of entanglement, and a simplified proof of the no-broadcasting theorem is obtained as a byproduct.
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"abstract": "Quantum theory can be regarded as a non-commutative generalization of\nclassical probability. From this point of view, one expects quantum dynamics to\nbe analogous to classical conditional probabilities. In this paper, a variant\nof the well-known isomorphism between completely positive maps and bipartite\ndensity operators is derived, which makes this connection much more explicit.\nThe new isomorphism is given an operational interpretation in terms of\nstatistical correlations between ensemble preparation procedures and outcomes\nof measurements. Finally, the isomorphism is applied to elucidate the\nconnection between no-cloning/no-broadcasting theorems and the monogamy of\nentanglement, and a simplified proof of the no-broadcasting theorem is obtained\nas a byproduct.",
"arxiv_id": "quant-ph/0606022",
"authors": [
"M. S. Leifer"
],
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"quant-ph"
],
"doi": "10.1103/PhysRevA.74.042310",
"journal_ref": "Phys. Rev. A 74, 042310 (2006)",
"title": "Quantum Dynamics as an analog of Conditional Probability",
"url": "https://arxiv.org/abs/quant-ph/0606022"
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