Quantum channels and memory effects

Filippo Caruso, Vittorio Giovannetti, Cosmo Lupo, and Stefano Mancini
Rev. Mod. Phys. 86, 1203 – Published 10 December 2014

Abstract

Any physical process can be represented as a quantum channel mapping an initial state to a final state. Hence it can be characterized from the point of view of communication theory, i.e., in terms of its ability to transfer information. Quantum information provides a theoretical framework and the proper mathematical tools to accomplish this. In this context the notion of codes and communication capacities have been introduced by generalizing them from the classical Shannon theory of information transmission and error correction. The underlying assumption of this approach is to consider the channel not as acting on a single system, but on sequences of systems, which, when properly initialized allow one to overcome the noisy effects induced by the physical process under consideration. While most of the work produced so far has been focused on the case in which a given channel transformation acts identically and independently on the various elements of the sequence (memoryless configuration in jargon), correlated error models appear to be a more realistic way to approach the problem. A slightly different, yet conceptually related, notion of correlated errors applies to a single quantum system which evolves continuously in time under the influence of an external disturbance which acts on it in a non-Markovian fashion. This leads to the study of memory effects in quantum channels: a fertile ground where interesting novel phenomena emerge at the intersection of quantum information theory and other branches of physics. A survey is taken of the field of quantum channels theory while also embracing these specific and complex settings.

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  • Received 16 July 2012

DOI:https://doi.org/10.1103/RevModPhys.86.1203

© 2014 American Physical Society

Authors & Affiliations

Filippo Caruso*

  • QSTAR, Largo Enrico Fermi 2, I-50125 Firenze, Italy, LENS and Università di Firenze, via Carrara 1, I-50019 Sesto Fiorentino, Italy, Dipartimento di Fisica e Astronomia, Università di Firenze, via Sansone 1, I-50019 Sesto Fiorentino, Italy, and Institut für Theoretische Physik, Universität Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany

Vittorio Giovannetti

  • NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, Piazza dei Cavalieri 7, I-56126 Pisa, Italy

Cosmo Lupo

  • MIT, Research Laboratory of Electronics, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA, and School of Science and Technology, University of Camerino, I-62032 Camerino, Italy

Stefano Mancini§

  • School of Science and Technology, University of Camerino, I-62032 Camerino, Italy and INFN-Sezione di Perugia, Via A. Pascoli, I-06123 Perugia, Italy

  • *filippo.caruso@lens.unifi.it
  • v.giovannetti@sns.it
  • cosmo.lupo@unicam.it
  • §stefano.mancini@unicam.it

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Vol. 86, Iss. 4 — October - December 2014

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