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arXiv:1511.05308 · Physical Review A

Information, fidelity, and reversibility in general quantum measurements

Hiroaki Terashima

Published Feb 3, 2016• 17 citations
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Abstract

We present the amount of information, fidelity, and reversibility obtained by arbitrary quantum measurements on completely unknown states. These quantities are expressed as functions of the singular values of a measurement operator corresponding to the obtained outcome. As an example, we consider a class of quantum measurements with highly degenerate singular values to discuss trade-offs among information, fidelity, and reversibility. The trade-offs are at the level of a single outcome, in the sense that the quantities pertain to each single outcome rather than the average over all possible outcomes.

DOI
10.1103/physreva.93.022104

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We present the amount of information, fidelity, and reversibility obtained by arbitrary quantum measurements on completely unknown states. These quantities are expressed as functions of the singular values of a measurement operator corresponding to the obtained outcome. As an example, we consider a class of quantum measurements with highly degenerate singular values to discuss trade-offs among information, fidelity, and reversibility. The trade-offs are at the level of a single outcome, in the sense that the quantities pertain to each single outcome rather than the average over all possible outcomes.
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It is of general interest how a quantum measurement may disturb a quantum system while it gives information on the state of the system. We study a trade-off relation between the information gain and the output fidelity for a quantum nondemolition measurement scheme for photon numbers. Toward this aim, we obtain general expressions for the information gain and the output fidelity for an arbitrary initial state. We particularly investigate how these two quantities vary with measurement strength for some specific classes of states, through a single measurement or successive measurements.
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