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Chinese Physics Letters

Locally Accessible Information from Multipartite Ensembles

Song Wei

Published Jun 1, 2009• 0 citations
Publisher

Abstract

We present a universal Holevo-like upper bound on the locally accessible information for arbitrary multipartite ensembles. This bound allows us to analyze the indistinguishability of a set of orthogonal states under local operations and classical communication. We also derive the upper bound for the capacity of distributed dense coding with multipartite senders and multipartite receivers.

DOI
10.1088/0256-307x/26/6/060303

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We present a universal Holevo-like upper bound on the locally accessible information for arbitrary multipartite ensembles. This bound allows us to analyze the indistinguishability of a set of orthogonal states under local operations and classical communication. We also derive the upper bound for the capacity of distributed dense coding with multipartite senders and multipartite receivers.
We introduce the notion of distributed quantum dense coding, i.e., the generalization of quantum dense coding to more than one sender and more than one receiver. We show that global operations (as compared to local operations) of the senders do not increase the information transfer capacity, in the case of a single receiver. For the case of two receivers, using local operations and classical communication, a nontrivial upper bound for the capacity is derived. We propose a general classification scheme of quantum states according to their usefulness for dense coding. In the bipartite case (for any dimensions), bound entanglement is not useful for this task.
We consider generalizations of the dense coding protocol with an arbitrary number of senders and either one or two receivers, sharing a multiparty quantum state, and using a noiseless channel. For the case of a single receiver, the capacity of such information transfer is found exactly. It is shown that the capacity is not enhanced by allowing the senders to perform joint operations. We provide a nontrivial upper bound on the capacity in the case of two receivers. We also give a classification of the set of all multiparty states in terms of their usefulness for dense coding. We provide examples for each of these classes, and discuss some of their properties.
I derive a universal upper bound on the capacity of any communication channel between two distant systems. The Holevo quantity, and hence the mutual information, is at most of order EΔt/ℏ, where E is the average energy of the signal, and Δt is the amount of time for which detectors operate. The bound does not depend on the size or mass of the emitting and receiving systems, nor on the nature of the signal. No restrictions on preparing and processing the signal are imposed. As an example, I consider the encoding of information in the transverse or angular position of a signal emitted and received by systems of arbitrarily large cross section. In the limit of a large message space, quantum effects become important even if individual signals are classical, and the bound is upheld.