Exact non-Markovian master equations for multiple qubit systems: Quantum-trajectory approach

Abstract

A wide class of exact master equations for a multiple qubit system can be explicitly constructed by using the corresponding exact non-Markovian quantum-state diffusion equations. These exact master equations arise naturally from the quantum decoherence dynamics of qubit system as a quantum memory coupled to a collective colored noisy source. The exact master equations are also important in optimal quantum control, quantum dissipation, and quantum thermodynamics. In this paper, we show that the exact non-Markovian master equation for a dissipative N -qubit system can be derived explicitly from the statistical average of the corresponding non-Markovian quantum trajectories. We illustrated our general formulation by an explicit construction of a three-qubit system coupled to a non-Markovian bosonic environment. This multiple qubit master equation offers an accurate time evolution of quantum systems in various domains, and paves the way to investigate the memory effect of an open system in a non-Markovian regime without any approximation.

Impact of the central frequency of environment on non-Markovian dynamics in piezoelectric optomechanical devices

“…Each numerical solution of the SSE is so-called a trajectory and the reduced density operator of the system can be reproduced by taking average of all trajectories. Moreover, the corresponding master equation can be obtained formally 50 , 61 , 62 . Secondly, we investigate how the entanglement is influenced by various non-Markovian environment 51 , 52 .…”

“…In this section, we briefly review the relevant background of non-Markovian dynamics, particularly using the quantum-state diffusion (QSD) approach and the corresponding master equation (MEQ) approach 50 , 61 , 63 .…”

Effect of Time-Delayed Feedback on the Interaction of a Dimer System with its Environment

“…Unlike Markovian quantum systems, where deriving memory-less equations of motion is a feasible task 27 – 29 , the study of open quantum systems with random memory (or quantum feedback) effect is more elusive, because of the absence of systematic tools independent of the system-environment specific interaction 30 , 31 . In this context, Carmichael, Gardiner, and Sokolov, independently developed the theory of cascaded quantum open systems 32 – 34 where typically the output from one system is fed into another one.…”

Memory-effect-induced macroscopic-microscopic entanglement

“…Alternatively, one can also use the NMQSD equation to derive the corresponding exact master equation for the system by following the method in Ref. [40,48]. In this paper, we will take a straightforward step to truncate the O operator to the noise free terms, called the zeroth order approximation, which turns out to be appropriate for many practical purposes as discussed in Ref.…”

“…The advantage of the exact treatment is that the memory effect in this model can be treated in a systematic way without introducing any _ ad hoc parameters to represent the environmental noises. We shall use the non-Markovian quantum state diffusion (NMQSD) equation to solve quantum open systems coupled to a non-Markovian bosonic or fermionic environment [36][37][38][39][40][41][42][43][44][45][46][47][48][49]. Such a stochastic approach provides a very powerful tool in both analytical treatments and numerical simulations, especially in dealing with the non-Markovian perturbation and solving the corresponding master equation for the open quantum systems.…”