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Journal of Physics A Mathematical and General

The classical capacity of a quantum dense coding system

Masashi Ban, Sachiko Kitajima, Fumiaki Shibata

Published Aug 18, 2004• 5 citations
Publisher

Abstract

Quantum dense coding transmits classical information by sending a quantum system with the assistance of quantum entanglement. The classical information capacity of a quantum dense coding system is obtained, where a sender and receiver share a completely entangled state and a quantum system encoded by applying unitary operators is sent through an arbitrary quantum channel. The result is compared with that obtained in another setting.

DOI
10.1088/0305-4470/37/35/l01

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Quantum dense coding transmits classical information by sending a quantum system with the assistance of quantum entanglement. The classical information capacity of a quantum dense coding system is obtained, where a sender and receiver share a completely entangled state and a quantum system encoded by applying unitary operators is sent through an arbitrary quantum channel. The result is compared with that obtained in another setting.
One of the primary goals of information theory is to provide limits on the amount of information one can send through communication channels, and to understand encoding methods that achieve such limits. The discovery of dense coding showed that quantum channels can transmit twice as much classical information than is possible with a classical channel. This optimal rate requires using quantum systems maximally entangled between sender and receiver, and then the sender can encode her messages using unitary operations. The use of nonmaximally entangled systems has been intensively studied in recent years, and it has appeared as though unitary encoding might well be optimal in all cases. Indeed, this optimality of unitary operations has been found to hold under far more general conditions. Nonetheless, we here present numerical evidence supported by analytical arguments that there exist circumstances where more classical information can be encoded using nonunitary, rather than unitary, operations.
The quantum advantage of dense coding—the increase in the rate of classical information transmission due to shared entanglement—is studied. General encoding quantum operations are considered. Particular attention is devoted to the case of many senders and one receiver. It is shown that restrictions on the possible operations among the many senders can strongly affect the usefulness of a shared quantum state for dense coding. It is shown, e.g., that there are states that do not provide any quantum advantage if communication among the senders is not allowed, but are useful for dense coding as soon as the senders can communicate classically. These results are actually independent of the particular quantification of the quantum advantage, being valid for any reasonable definition of such a rate increase. It is further shown that the quantum advantage of dense coding satisfies a monogamy relation with the so-called entanglement of purification.
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.