Deterministic quantum master equation for non-Markovian signal processing

TL;DR

This paper derives a deterministic master equation to model non-Markovian feedback in quantum systems, enabling better understanding of systems with memory effects and complex frequency-dependent feedback mechanisms.

Contribution

It introduces a novel master equation framework that captures non-Markovian feedback processes with arbitrary structure and dimensionality, advancing quantum signal processing modeling.

Findings

The master equation effectively models systems with memory feedback.

Examples demonstrate the equation's ability to handle non-trivial frequency dependence.

The approach generalizes existing models to include arbitrary non-Markovian feedback.

Abstract

In this work, we derive a deterministic master equation to model a general, possibly non-Markovian, feedback. The master equation describes a system with a general evolution and measurement operation, with feedback being applied in terms of signal processing. The feedback signal has an arbitrary structure with dimensionality that indicates the degree of non-Markovianity of the information processing. We present examples to illustrate how such a master equation can be used to model systems with memory feedback and non-trivial frequency dependence.