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arXiv:quant-ph/0409217

POVM optimization of classical correlations

S. Hamieh, R. Kobes, Haitham Zaraket

Published Sep 30, 2004• 0 citations
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Abstract

We study the problem of optimization over positive valued-operator measure to extract classical correlation in a bipartite quantum system. The proposed method is applied to binary states only. Moreover, to illustrate this method, an explicit example is studied in details.
DOI
10.48550/arxiv.quant-ph/0409217

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Abstract We give a brief summary of the current status of the problem of extracting the accessible information when a quantum system is received in one of a finite number of pre-known quantum states. We review analytical methods as well as a numerical strategy. In particular, the group-covariant positive-operator-valued measures are discussed, and several explicit examples are worked out in detail. These examples include some that occur in the security analysis of schemes for quantum cryptography.
The expectation value of an arbitrary operator O can be obtained via a universal measuring apparatus that is independent of O, by changing only the data-processing of the outcomes. Such a ``universal detector'' performs a joint measurement on the system and on a suitable ancilla prepared in a fixed state, and is equivalent to a positive operator valued measure (POVM) for the system that is ``informationally complete''. The data processing functions generally are not unique, and we pose the problem of their optimization, providing some examples for covariant POVM's, in particular for SU(d) covariance group.
Various forms of optimality for quantum observables described as normalized positive-operator-valued measures (POVMs) are studied in this paper. We give characterizations for observables that determine the values of the measured quantity with probabilistic certainty or a state of the system before or after the measurement. We investigate observables that are free from noise caused by classical post-processing, mixing, or pre-processing of quantum nature. Especially, a complete characterization of pre-processing and post-processing clean observables is given, and necessary and sufficient conditions are imposed on informationally complete POVMs within the set of pure states. We also discuss joint and sequential measurements of optimal quantum observables.