Quantum dynamics as an analog of conditional probability

M. S. Leifer
Phys. Rev. A 74, 042310 – Published 12 October 2006

Abstract

Quantum theory can be regarded as a noncommutative 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. This 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 and no-broadcasting theorems and the monogamy of entanglement, and a simplified proof of the no-broadcasting theorem is obtained as a by-product.

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  • Received 14 June 2006

DOI:https://doi.org/10.1103/PhysRevA.74.042310

©2006 American Physical Society

Authors & Affiliations

M. S. Leifer*

  • Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, Canada N2L 2Y5

  • *Electronic address: mleifer@perimeterinstitute.ca

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Vol. 74, Iss. 4 — October 2006

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