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Springer eBooks

Information Gain in Quantum Communication Channels

Giacomo Mauro D’Ariano, Chiara Macchiavello, Matteo G. A. Paris

Published Jan 1, 1995• 6 citations
Publisher
DOI
10.1007/978-1-4899-1391-3_32

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Journal of Information Security and Cryptography (Enigma)•Dec 7, 2015•0 citations
We show that quantum-to-classical channels, i.e., quantum measurements, can be asymptotically simulated by an amount of classical communication equal to the quantum mutual information of the measurement, if sufficient shared randomness is available. This result generalizes Winter's measurement compression theorem for fixed independent and identically distributed inputs [Winter, CMP 244 (157), 2004] to arbitrary inputs, and more importantly, it identifies the quantum mutual information of a measurement as the information gained by performing it, independent of the input state on which it is performed. Our result is a generalization of the classical reverse Shannon theorem to quantum-to-classical channels. In this sense, it can be seen as a quantum reverse Shannon theorem for quantum-to-classical channels, but with the entanglement assistance and quantum communication replaced by shared randomness and classical communication, respectively. Our proof is based on quantum-proof randomness extractors and the post-selection technique for quantum channels [Christandl et al., PRL 102 (020504), 2009].
We show that quantum-to-classical channels, i.e., quantum measurements, can be asymptotically simulated by an amount of classical communication equal to the quantum mutual information of the measurement, if sufficient shared randomness is available. This result generalizes Winter's measurement compression theorem for fixed independent and identically distributed inputs to arbitrary inputs, and more importantly, it identifies the quantum mutual information of a measurement as the information gained by performing it, independent of the input state on which it is performed. Our result is a generalization of the classical reverse Shannon theorem to quantum-to-classical channels. In this sense, it can be seen as a quantum reverse Shannon theorem for quantum-to-classical channels, but with the entanglement assistance and quantum communication replaced by shared randomness and classical communication, respectively. The proof is based on a novel one-shot state merging protocol for classically coherent states as well as the postselection technique for quantum channels, and it uses techniques developed for the quantum reverse Shannon theorem.
We show how to use decoherence-free subspaces over collective-noise quantum channels to convey classical information in perfect secrecy. We argue that codes defined over decoherence-free subspaces are codes for quantum wiretap channels in which the gain of information by a non-authorized third part is zero. We also show that if some symmetry conditions are guaranteed, the maximum rate on which such secret communications take place is equal to the ordinary capacity of a quantum channel to convey classical information. As a consequence of these results, we show how some protocols for secure communication can be simplified, reducing significantly the number of communications performed.