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Title: On the constrained classical capacity of infinite-dimensional covariant quantum channels

Abstract

The additivity of the minimal output entropy and that of the χ-capacity are known to be equivalent for finite-dimensional irreducibly covariant quantum channels. In this paper, we formulate a list of conditions allowing to establish similar equivalence for infinite-dimensional covariant channels with constrained input. This is then applied to bosonic Gaussian channels with quadratic input constraint to extend the classical capacity results of the recent paper [Giovannetti et al., Commun. Math. Phys. 334(3), 1553-1571 (2015)] to the case where the complex structures associated with the channel and with the constraint operator need not commute. In particular, this implies a multimode generalization of the “threshold condition,” obtained for single mode in Schäfer et al. [Phys. Rev. Lett. 111, 030503 (2013)], and the proof of the fact that under this condition the classical “Gaussian capacity” resulting from optimization over only Gaussian inputs is equal to the full classical capacity. Complex structures correspond to different squeezings, each with its own normal modes, vacuum and coherent states, and the gauge. Thus our results apply, e.g., to multimode channels with a squeezed Gaussian noise under the standard input energy constraint, provided the squeezing is not too large as to violate the generalized threshold condition. Wemore » also investigate the restrictiveness of the gauge-covariance condition for single- and multimode bosonic Gaussian channels.« less

Authors:
 [1]
  1. Steklov Mathematical Institute, 119991 Moscow (Russian Federation)
Publication Date:
OSTI Identifier:
22479610
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 57; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANNIHILATION OPERATORS; EIGENSTATES; ENTROPY; LIMITING VALUES; NOISE; OPTIMIZATION

Citation Formats

Holevo, A. S. On the constrained classical capacity of infinite-dimensional covariant quantum channels. United States: N. p., 2016. Web. doi:10.1063/1.4928050.
Holevo, A. S. On the constrained classical capacity of infinite-dimensional covariant quantum channels. United States. https://doi.org/10.1063/1.4928050
Holevo, A. S. 2016. "On the constrained classical capacity of infinite-dimensional covariant quantum channels". United States. https://doi.org/10.1063/1.4928050.
@article{osti_22479610,
title = {On the constrained classical capacity of infinite-dimensional covariant quantum channels},
author = {Holevo, A. S.},
abstractNote = {The additivity of the minimal output entropy and that of the χ-capacity are known to be equivalent for finite-dimensional irreducibly covariant quantum channels. In this paper, we formulate a list of conditions allowing to establish similar equivalence for infinite-dimensional covariant channels with constrained input. This is then applied to bosonic Gaussian channels with quadratic input constraint to extend the classical capacity results of the recent paper [Giovannetti et al., Commun. Math. Phys. 334(3), 1553-1571 (2015)] to the case where the complex structures associated with the channel and with the constraint operator need not commute. In particular, this implies a multimode generalization of the “threshold condition,” obtained for single mode in Schäfer et al. [Phys. Rev. Lett. 111, 030503 (2013)], and the proof of the fact that under this condition the classical “Gaussian capacity” resulting from optimization over only Gaussian inputs is equal to the full classical capacity. Complex structures correspond to different squeezings, each with its own normal modes, vacuum and coherent states, and the gauge. Thus our results apply, e.g., to multimode channels with a squeezed Gaussian noise under the standard input energy constraint, provided the squeezing is not too large as to violate the generalized threshold condition. We also investigate the restrictiveness of the gauge-covariance condition for single- and multimode bosonic Gaussian channels.},
doi = {10.1063/1.4928050},
url = {https://www.osti.gov/biblio/22479610}, journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 1,
volume = 57,
place = {United States},
year = {Fri Jan 15 00:00:00 EST 2016},
month = {Fri Jan 15 00:00:00 EST 2016}
}