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Majorization and additivity for multimode bosonic Gaussian channels

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Abstract

We obtain a multimode extension of the majorization theorem for bosonic Gaussian channels, in particular, giving sufficient conditions under which the Glauber coherent states are the only minimizers for concave functionals of the output state of such a channel. We discuss direct implications of this multimode majorization for the positive solution of the famous additivity problem in the case of Gaussian channels. In particular, we prove the additivity of the output Rényi entropies of arbitrary order p > 1. Finally, we present an alternative, more direct derivation of a majorization property of the Husimi function established by Lieb and Solovej.

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Authors and Affiliations

  1. NEST, Scuola Normale Superiore e Istituto Nanoscienze-CNR, Pisa, Italy

    V. Giovannetti & A. Mari

  2. Steklov Mathematical Institute, RAS, Moscow, Russia

    A. S. Holevo

Authors
  1. V. Giovannetti
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  2. A. S. Holevo
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  3. A. Mari
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Corresponding author

Correspondence to A. S. Holevo.

Additional information

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 182, No. 2, pp. 338–349, February, 2015.

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Giovannetti, V., Holevo, A.S. & Mari, A. Majorization and additivity for multimode bosonic Gaussian channels. Theor Math Phys 182, 284–293 (2015). https://doi.org/10.1007/s11232-015-0262-6

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  • DOI: https://doi.org/10.1007/s11232-015-0262-6

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