Dynamical invariants in non-Markovian quantum state diffusion equation

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.

6 pages, 2 figures

References in corpus (15)

• Non-Markovian effects on the dynamics of entanglement
• Environment-Assisted Quantum Transport
• Lewis-Riesenfeld invariants and transitionless tracking algorithm
• Non-Markovian quantum jumps
• Experimental on-demand recovery of entanglement by local operations within non-Markovian dynamics
• Non-Markovian Relaxation of a Three-Level System: Quantum Trajectory Approach
• Pure-state quantum trajectories for general non-Markovian systems do not exist
• Non-Markovian continuous quantum measurement of retarded observables
• Nonperturbative Leakage Elimination Operators and Control of a Three-Level System
• Exact non-Markovian master equations for multiple qubit systems: quantum trajectory approach
• Fermionic Stochastic Schrödinger Equation and Master Equation: An Open System Model
• Long-range entanglement generation via frequent measurements
• Dynamical invariants and nonadiabatic geometric phases in open quantum systems
• Approach to solving spin-boson dynamics via non-Markovian quantum trajectories
• Higher-order solutions to non-Markovian quantum dynamics via hierarchical functional derivative

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• Universal quantum control by non-Hermitian Hamiltonian
• Quantum mechanics and speed limit of ultrafast local control in spin chains
• Positivity Preserving non-Markovian Master Equation for Open Quantum System Dynamics: Stochastic Schrödinger Equation Approach
• Tunable Tradeoff between Quantum and Classical Computation via Nonunitary Zeno-like Dynamics
• Quantum Transport Protected by Acceleration From Nonadiabaticity and Dissipation