Dynamical invariants in non-Markovian quantum state diffusion equation

TL;DR

This paper introduces dynamical invariants for non-Markovian quantum systems described by the QSD equation, enabling exact solutions and new control strategies without relying on master equations or simulations.

Contribution

It presents a novel method to find dynamical invariants in non-Markovian quantum systems, facilitating exact solutions and system control design.

Findings

Dynamical invariants differ from density operators in non-Markovian systems.

Invariants from bi-orthonormal basis enable exact solutions to QSD equations.

Application of invariants allows reverse-engineering of Hamiltonians for system control.

Abstract

We find dynamical invariants for open quantum systems described by the non-Markovian quantum state diffusion (QSD) equation. In stark contrast to closed systems where the dynamical invariant can be identical to the system density operator, these dynamical invariants no longer share the equation of motion for the density operator. Moreover, the invariants obtained with from bi-orthonormal basis can be used to render an exact solution to the QSD equation and the corresponding non-Markovian dynamics without using master equations or numerical simulations. Significantly we show that we can apply these dynamic invariants to reverse-engineering a Hamiltonian that is capable of driving the system to the target state, providing a novel way to design control strategy for open quantum systems.