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Deterministic quantum master equation for non-Markovian signal processing

Guilherme de Sousa, Diogo O. Soares-Pinto

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.

Deterministic quantum master equation for non-Markovian signal processing

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.
Paper Structure (7 sections, 18 equations, 1 figure)

This paper contains 7 sections, 18 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Outline of the derivation
  3. Application to non-Markovian feedback
  4. Feedback rule with momentum
  5. Feedback rule with $T$ steps in the past
  6. Discussion and outlook
  7. Derivation

Figures (1)

  • Figure 1: Steps for evolving the conditional quantum state from one observation at $t_n$ to the next observation at $t_{n+1}$. The sequence involves (a) measuring using the Kraus operators, (b) collecting and processing the information using non-Markovian feedback rule, and (c) applying feedback based on the Markovian embedded high-dimensional signal.