Majorization theory approach to the Gaussian channel minimum entropy conjecture |
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Authors: | García-Patrón Raúl Navarrete-Benlloch Carlos Lloyd Seth Shapiro Jeffrey H Cerf Nicolas J |
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Institution: | Research Laboratory of Electronics, MIT, Cambridge, Massachusetts 02139, USA. |
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Abstract: | A long-standing 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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