Expectation Synchronization Synthesis in Non-Markovian Open Quantum Systems

TL;DR

This paper develops a method to engineer quantum synchronization in non-Markovian systems by deriving a stochastic differential equation and designing system parameters, enabling synchronization without direct coupling under certain conditions.

Contribution

It introduces a novel approach to synthesize quantum expectation synchronization in non-Markovian systems without direct Hamiltonian coupling, based on explicit parameter design.

Findings

Synchronization can be achieved without direct Hamiltonian coupling for low non-Markovianity.

Explicit system parameters are provided for synchronization.

Numerical example validates the theoretical results.

Abstract

In this article, we investigate the problem of engineering synchronization in non-Markovian quantum systems. First, a time-convoluted linear quantum stochastic differential equation is derived which describes the Heisenberg evolution of a localized quantum system driven by multiple colored noise inputs. Then, we define quantum expectation synchronization in an augmented system consisting of two subsystems. We prove that, for two homogenous subsystems, synchronization can always be synthesized without designing direct Hamiltonian coupling given that the degree of non-Markovianity is below a certain threshold. System parameters are explicitly designed to achieve quantum synchronization. Also, a numerical example is presented to illustrate our results.