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arXiv · 1111.1986

Majorization theory approach to the Gaussian channel minimum entropy conjecture

Raul Garcia-Patron·Carlos Navarrete-Benlloch·Seth Lloyd·Jeffrey H. Shapiro·Nicolas J. Cerf
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Abstract

A longstanding open problem in quantum information theory is to find the classical capacity of an optical communication link, modeled as a Gaussian bosonic channel. It has been conjectured that this capacity is achieved by a random coding of coherent states using an isotropic Gaussian distribution in phase space. We show that proving a Gaussian minimum entropy conjecture for a quantum-limited amplifier is actually sufficient to confirm this capacity conjecture, and we provide a strong argument towards this proof by exploiting a connection between quantum entanglement and majorization theory.

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Raul Garcia-Patron, Carlos Navarrete-Benlloch, Seth Lloyd, Jeffrey H. Shapiro, Nicolas J. Cerf. 2011-11-08. Majorization theory approach to the Gaussian channel minimum entropy conjecture. https://doi.org/10.1103/physrevlett.108.110505

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