Maximum Quantum Entropy Method

TL;DR

This paper introduces a quantum relative entropy extension to the maximum entropy method, enabling more straightforward continuation of off-diagonal elements while maintaining Bayesian interpretation, demonstrated on model and real spectra.

Contribution

The paper presents a novel quantum relative entropy-based extension of the maximum entropy method, formulated with matrix-valued functions for improved analytic continuation.

Findings

Enhanced continuation of off-diagonal elements in spectra.

Maintains Bayesian probabilistic interpretation.

Proven usefulness and superiority on model and real data.

Abstract

Maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This new method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input matrix. As a result, the continuation of off-diagonal elements becomes straightforward. Without introducing any further ambiguity, the Bayesian probabilistic interpretation is maintained just as in the conventional maximum entropy method. The applications of our generalized formalism to a model spectrum and a real material demonstrate its usefulness and superiority.