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Quantum extension of conditional probability

Cerf, N. J. and Adami, C. (1999) Quantum extension of conditional probability. Physical Review A, 60 (2). pp. 893-897. ISSN 1050-2947. doi:10.1103/PhysRevA.60.893.

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We analyze properties of the quantum conditional amplitude operator [Phys. Rev. Lett. 79, 5194 (1997)], which plays a role similar to that of the conditional probability in classical information theory. The spectrum of the conditional operator that characterizes a quantum bipartite system is shown to be invariant under local unitary transformations and reflects its inseparability. More specifically, it is proven that the conditional amplitude operator of a separable state cannot have an eigenvalue exceeding 1, which results in a necessary condition for separability. A related separability criterion based on the non-negativity of the von Neumann conditional entropy is also exhibited.

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Adami, C.0000-0002-2915-9504
Additional Information:©1999 The American Physical Society. Received 31 October 1997; revised 14 December 1998. We acknowledge useful discussions with Lev Levitin, Barry Simon, and Armin Uhlmann. This work was supported in part by NSF Grant Nos. PHY 94-12818 and PHY 94-20470, and by a grant from DARPA/ARO through the QUIC Program (No. DAAH04-96-1-3086).
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2322
Deposited By: Tony Diaz
Deposited On:27 Mar 2006
Last Modified:08 Nov 2021 19:46

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