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arXiv:quant-ph/0304040 · Physical Review Letters

Locally Accessible Information: How Much Can the Parties Gain by Cooperating?

Piotr Badziąg, Michał Horodecki, Aditi Sen, Ujjwal Sen

Published Sep 9, 2003• 48 citations
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Abstract

We investigate measurements of bipartite ensembles restricted to local operations and classical communication and find a universal Holevo-like upper bound on the locally accessible information. We analyze our bound and exhibit a class of states which saturate it. Finally, we link the bound to the problem of quantification of the nonlocality of the operations necessary to extract locally inaccessible information.

DOI
10.1103/physrevlett.91.117901

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We investigate measurements of bipartite ensembles restricted to local operations and classical communication and find a universal Holevo-like upper bound on the locally accessible information. We analyze our bound and exhibit a class of states which saturate it. Finally, we link the bound to the problem of quantification of the nonlocality of the operations necessary to extract locally inaccessible information.
We find a universal lower bound on locally accessible information for arbitrary bipartite ensembles, when one of the parties is two-dimensional. In higher dimensions and in higher number of parties, the lower bound is on accessible information by separable operations. We evaluate this bound for several ensembles, for which the exact locally accessible information is not known. We show that for any given density matrix (of arbitrary number of parties and dimensions), there exists an ensemble, the so-called ``Scrooge ensemble'', which averages to the given density matrix and whose locally accessible information saturates the lower bound.
We find a universal lower bound on locally accessible information for arbitrary bipartite quantum ensembles, when one of the parties is two dimensional. In higher dimensions and in a higher number of parties, the bound is on accessible information by separable operations. We show that for any given density matrix (of an arbitrary number of parties and dimensions), there exists an ensemble, which averages to the given density matrix and whose locally accessible information saturates the lower bound. Moreover, we give a general method to obtain bounds on the yield of singlets in distillation protocols that involves local distinguishing, by using lower and upper bounds on locally accessible information. We then illustrate it by using our lower bound, along with a previously obtained upper bound, on locally accessible information.
Because of the importance of entanglement for quantum information purposes, a framework has been developed for its characterization and quantification as a resource based on the following operational principle: entanglement among N parties cannot be created by local operations and classical communication, even when N-1 parties collaborate. More recently, nonlocality has been identified as another resource, alternative to entanglement and necessary for device-independent quantum information protocols. We introduce an operational framework for nonlocality based on a similar principle: nonlocality among N parties cannot be created by local operations and allowed classical communication even when N-1 parties collaborate. We then show that the standard definition of multipartite nonlocality, due to Svetlichny, is inconsistent with this operational approach: according to it, genuine tripartite nonlocality could be created by two collaborating parties. We finally discuss alternative definitions for which consistency is recovered.