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Rep. Progr. Phys., 2012, Volume 75, Pages 46001–45 (Mi rpph1)  

Quantum channels and their entropic characteristics

A. S. Holevoa, V. Giovannettib

a Steklov Mathematical Institute, Gubkina 8, 119991 Moscow, Russia
b NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, piazza dei Cavalieri 7, I-56126 Pisa, Italy

Abstract: One of the major achievements of the recently emerged quantum information theory is the introduction and thorough investigation of the notion of a quantum channel which is a basic building block of any data-transmitting or data-processing system. This development resulted in an elaborated structural theory and was accompanied by the discovery of a whole spectrum of entropic quantities, notably the channel capacities, characterizing information-processing performance of the channels. This paper gives a survey of the main properties of quantum channels and of their entropic characterization, with a variety of examples for finite-dimensional quantum systems. We also touch upon the ‘continuous-variables’ case, which provides an arena for quantum Gaussian systems. Most of the practical realizations of quantum information processing were implemented in such systems, in particular based on principles of quantum optics. Several important entropic quantities are introduced and used to describe the basic channel capacity formulae. The remarkable role of specific quantum correlations—entanglement—as a novel communication resource is stressed.

Funding Agency Grant Number
Italian Ministry of Education, University and Research RBID08B3FM
Russian Foundation for Basic Research
Russian Academy of Sciences - Federal Agency for Scientific Organizations
VG acknowledges support from MIUR through FIRB-IDEAS Project No RBID08B3FM. AH was partially supported by an RFBR grant and the RAS program 'Dynamical systems and control theory'.


DOI: https://doi.org/10.1088/0034-4885/75/4/046001


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Received: 25.08.2011
Revised: 15.11.2011
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