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Dividing Quantum Channels

Communications in Mathematical Physics volume 279, pages 147–168 (2008)Cite this article

Abstract

We investigate the possibility of dividing quantum channels into concatenations of other channels, thereby studying the semigroup structure of the set of completely-positive trace-preserving maps. We show the existence of ‘indivisible’ channels which can not be written as non-trivial products of other channels and study the set of ‘infinitesimal divisible’ channels which are elements of continuous completely positive evolutions. For qubit channels we obtain a complete characterization of the sets of indivisible and infinitesimal divisible channels. Moreover, we identify those channels which are solutions of time-dependent master equations for both positive and completely positive evolutions. For arbitrary finite dimension we prove a representation theorem for elements of continuous completely positive evolutions based on new results on determinants of quantum channels and Markovian approximations.

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Authors and Affiliations

  1. Max-Planck-Institute for Quantum Optics, Hans-Kopfermann-Str. 1, 85748, Garching, Germany

    Michael M. Wolf & J. Ignacio Cirac

Authors
  1. Michael M. Wolf
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  2. J. Ignacio Cirac
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Correspondence to Michael M. Wolf.

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Communicated by M.B. Ruskai

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Wolf, M.M., Cirac, J.I. Dividing Quantum Channels. Commun. Math. Phys. 279, 147–168 (2008). https://doi.org/10.1007/s00220-008-0411-y

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  • DOI: https://doi.org/10.1007/s00220-008-0411-y

Keywords

  • Quantum Channel
  • Positive Evolution
  • Trace Preserve
  • Markovian Approximation
  • Positive Operator Value Measure