Control of the von Neumann Entropy for an Open Two-Qubit System Using Coherent and Incoherent Drives

TL;DR

This paper develops methods to control the von Neumann entropy of an open two-qubit system using coherent and incoherent drives, enabling targeted entropy manipulation under Markovian dynamics.

Contribution

It introduces a novel control approach for entropy management in open quantum systems using gradient and genetic algorithms.

Findings

Effective entropy minimization and maximization achieved.

Successful steering of entropy to target values demonstrated.

Numerical methods adapted for specific entropy control objectives.

Abstract

This article is devoted to developing an approach for manipulating the von Neumann entropy $S(\rho(t))$ of an open two-qubit system with coherent control and incoherent control inducing time-dependent decoherence rates. The following goals are considered: (a) minimizing or maximizing the final entropy $S(\rho(T))$; (b) steering $S(\rho(T))$ to a given target value; (c) steering $S(\rho(T))$ to a target value and satisfying the pointwise state constraint $S(\rho(t)) \leq \overline{S}$ for a given $\overline{S}$; (d) keeping $S(\rho(t))$ constant at a given time interval. Under the Markovian dynamics determined by a Gorini--Kossakowski--Sudarshan--Lindblad type master equation, which contains coherent and incoherent controls, one- and two-step gradient projection methods and genetic algorithm have been adapted, taking into account the specifics of the objective functionals. The corresponding numerical results are provided and discussed.