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Accessible information and optimal strategies for real symmetrical quantum sources

Masahide Sasaki·Stephen M. Barnett·Richard Jozsa·Masao Osaki·Osamu Hirota
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Abstract

We study the problem of optimizing the Shannon mutual information for sources of real quantum states i.e. sources for which there is a basis in which all the states have only real components. We consider in detail the sources ${\cal E}_M$ of $M$ equiprobable qubit states lying symmetrically around the great circle of real states on the Bloch sphere and give a variety of explicit optimal strategies. We also consider general real group-covariant sources for which the group acts irreducibly on the subset of all real states and prove the existence of a real group-covariant optimal strategy, extending a theorem of Davies (E. B. Davies, IEEE. Inf. Theory {\bf IT-24}, 596 (1978)). Finally we propose an optical scheme to implement our optimal strategies, enough simple to be realized with present technology.

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Masahide Sasaki, Stephen M. Barnett, Richard Jozsa, Masao Osaki, Osamu Hirota. 1999-01-18. Accessible information and optimal strategies for real symmetrical quantum sources. https://doi.org/10.1103/physreva.59.3325

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