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Characterizing mixing and measurement in quantum mechanics

Nielsen, M. A. (2001) Characterizing mixing and measurement in quantum mechanics. Physical Review A, 63 (2). Art. No. 022114. ISSN 1050-2947. doi:10.1103/PhysRevA.63.022114.

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What fundamental constraints characterize the relationship between a mixture ρ=∑ipiρi of quantum states, the states ρi being mixed, and the probabilities pi? What fundamental constraints characterize the relationship between prior and posterior states in a quantum measurement? In this paper we show that there are many surprisingly strong constraints on these mixing and measurement processes that can be expressed simply in terms of the eigenvalues of the quantum states involved. These constraints capture in a succinct fashion what it means to say that a quantum measurement acquires information about the system being measured, and considerably simplify the proofs of many results about entanglement transformation.

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Additional Information:©2001 The American Physical Society Received 16 August 2000; published 18 January 2001 Thanks to Dave Beckman, Sumit Daftuar, Julia Kempe, Beth Ruskai and Armin Uhlmann for discussions about majorization. Thanks also to Manny Knill for encouragement and bringing Ref. [20] to my attention, and to Chris Fuchs, Kurt Jacobs, and Reinhard Werner for bringing their unpublished work to my attention. This work was supported by a Tolman Fellowship, and by DARPA through the Quantum Information and Computing Institute (QUIC) administered through the ARO.
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Deposited On:27 Feb 2006
Last Modified:08 Nov 2021 19:44

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