Dissipative dynamics of an entangled three-qubit system via non-Hermitian Hamiltonian: Its correspondence with Markovian and non-Markovian regimes

Abstract

We investigate an entangled three-qubit system in which only one of the qubits experiences the decoherence effect by considering a non-Hermitian Hamiltonian, while the other two qubits are isolated, i.e., do not interact with environment, directly. Then, the time evolution of the density matrix (for the pure as well as mixed initial density matrix) and the corresponding reduced density matrices are obtained, by which we are able to utilize the dissipative non-Hermitian Hamiltonian model with Markovian and non-Markovian regimes via adjusting the strange of the non-Hermitian term of the total Hamiltonian of the under-considered system.

Model Hamiltonians of open quantum optical systems: Evolvement from hermiticity to adjoint commutativity

“…A modern version of the density operator approach with non-Hermitian Hamiltonians has been proposed relatively recently [4,5,6], where the normalization transformation was introduced. This immediately resulted in an outburst of applications, including entanglement's generation, amplification and protection, decoherence, spin squeezing, dissipative dimers, spin-chain-star systems, kicked rotor models, violations of Leggett-Garg inequality, population dynamics, Bayesian parameter estimation, modifications of the two-point measurement method, macroscopic quantum electrodynamics with a pseudomode, coherence delocalization in coupled-cavity systems, models with non-local initial conditions, nuclear spin ensemble with a reservoir, adiabaticity and entropy dynamics of various two-level dissipative systems, quantum Fisher information and phase estimation without and with decoherence, ground-state cooling of neardegenerate mechanical modes, to mention only a recent literature [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28].…”