Majorization theory approach to the Gaussian channel minimum entropy conjecture

TL;DR

This paper links the Gaussian minimum entropy conjecture for quantum-limited amplifiers to the classical capacity of optical channels, using majorization theory and quantum entanglement insights to advance understanding in quantum information theory.

Contribution

It establishes that proving the Gaussian minimum entropy conjecture suffices to confirm the classical capacity of Gaussian bosonic channels, connecting majorization theory with quantum communication.

Findings

Proposes a connection between quantum entanglement and majorization theory.

Argues that confirming the Gaussian minimum entropy conjecture would resolve the capacity problem.

Provides a theoretical framework linking entropy conjectures to channel capacity.

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.