Optimization of Quantum Information Processing Maximizing Mutual Information

TL;DR

This paper develops a model for optimizing quantum noisy channels by deriving equations for wave functions that maximize classical information transmission, providing solutions for Gaussian cases and suggesting physical implementations.

Contribution

It introduces an optimality equation for quantum decodings based on quasi-measurements and solves it for Gaussian channels, enhancing understanding of quantum information maximization.

Findings

Maximum classical information I=Spln[1+S/(N+1)] achieved

Optimal decoding uses overcomplete coherent vectors

Physical realization via heterodyne measurement suggested

Abstract

A model of quantum noisy channel with input encoding by a classical random vector is described. An equation of optimality is derived to determine a complete set of wave functions describing quantum decodings based on quasi-measurements maximizing the classical amount of transmitted information. A solution of this equation is found for the Gaussian multimode case with input Gaussian distribution. It is described by the overcomplete family of coherent vectors describing an optimal quasimeasurement of the canonical annihilation amplitudes in the output Hilbert space. It is found that the optimal decoding in this case realizes the maximum amount I=Spln[1+S/(N+1)] of the classical information as transmitted via the classical Gaussian channel with the effective noise covariance matrix N+I. A physical realization of optimal quasi-measurement based on an indirect (heterodyne) observation of the canonical operators is suggested.