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IEEE International Symposium on Information Theory (ISIT)

Classical capacity of quantum channels, coherent quantum information and quantum privacy

B. Schjumacher, Michael D. Westmorland

Published Nov 27, 2002• 0 citations
Publisher

Abstract

We derive a relation between a quantum channel's capacity to convey classical information and its ability to convey quantum information. This relation is applied to the analysis of the privacy of a quantum channel.
DOI
10.1109/isit.1998.708672

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A formula for the capacity of a quantum channel for transmitting private classical information is derived. This is shown to be equal to the capacity of the channel for generating a secret key, and neither capacity is enhanced by forward public classical communication. Motivated by the work of Schumacher and Westmoreland on quantum privacy and quantum coherence, parallels between private classical information and quantum information are exploited to obtain an expression for the capacity of a quantum channel for generating pure bipartite entanglement. The latter implies a new proof of the quantum channel coding theorem and a simple proof of the converse. The coherent information plays a role in all of the above mentioned capacities
Quantum technologies rely on the ability to coherently manipulate, process and transfer information, encoded in quantum states, along quantum channels. Decoherence induced by the environment introduces errors, thus setting limits on the efficiency of any quantum-enhanced protocol or device. A fundamental bound on the ability of a noisy quantum channel to transmit quantum (classical) information is given by its quantum (classical) capacity. Generally, the longer is a quantum channel the more are the introduced errors, and hence the worse is its capacity. In this Letter we show that for non-Markovian quantum channels this is not always true: surprisingly the capacity of a longer channel can be greater than the one of a shorter channel. We introduce a general theoretical framework linking non-Markovianity to the capacities of quantum channels, and demonstrate in full generality how harnessing non-Markovianity may improve the efficiency of quantum information processing and communication.
We study the power of quantum channels with little or no capacity for private communication. Because privacy is a necessary condition for quantum communication, one might expect that such channels would be of little use for transmitting quantum states. Nevertheless, we find strong evidence that there are pairs of such channels that, when used together, can transmit far more quantum information than the sum of their individual private capacities. Because quantum transmissions are necessarily private, this would imply a large violation of additivity for the private capacity. Specifically, we present channels which display either (1) a large joint quantum capacity but very small individual private capacities or (2) a severe violation of additivity for the Holevo information.