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Accessible information and optimal strategies for real symmetrical quantum sources
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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.
Forward citations
Cited by 2 Pith papers
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A conjecture on a tight norm inequality in the finite-dimensional l_p
A new tight inequality for l_p norms in finite-dimensional spaces is conjectured, proven for three dimensions, and numerically confirmed up to 200 dimensions with links to quantum entropy problems.
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New parametric entropy inequalities are derived from an accessible-information optimality criterion, reducing the quantum-pyramid conjecture to proving these inequalities.
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