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Expectation Synchronization Synthesis in Non-Markovian Open Quantum Systems

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.