State transfer in dissipative and dephasing environments

TL;DR

This paper investigates how dissipative and dephasing environments affect quantum state transfer and entanglement in spin networks, revealing environment-specific impacts and asymptotic behaviors as system size grows.

Contribution

It introduces a diagonalization method for the superoperator to analyze environment effects on quantum transfer and entanglement, highlighting differences between dissipative and dephasing impacts.

Findings

Dissipative environment causes more severe detrimental effects than dephasing.

Transfer fidelity at optimal time is independent of chain length under dissipation.

Maximum entanglement decreases with increasing chain length, approaching an environment-dependent asymptote.

Abstract

By diagonalization of a generalized superoperator for solving the master equation, we investigated effects of dissipative and dephasing environments on quantum state transfer, as well as entanglement distribution and creation in spin networks. Our results revealed that under the condition of the same decoherence rate $\gamma$, the detrimental effects of the dissipative environment are more severe than that of the dephasing environment. Beside this, the critical time $t_c$ at which the transfer fidelity and the concurrence attain their maxima arrives at the asymptotic value $t_0=\pi/2\lambda$ quickly as the spin chain length $N$ increases. The transfer fidelity of an excitation at time $t_0$ is independent of $N$ when the system subjects to dissipative environment, while it decreases as $N$ increases when the system subjects to dephasing environment. The average fidelity displays three different patterns corresponding to $N=4r+1$, $N=4r-1$ and $N=2r$. For each pattern, the average fidelity at time $t_0$ is independent of $r$ when the system subjects to dissipative environment, and decreases as $r$ increases when the system subjects to dephasing environment. The maximum concurrence also decreases as $N$ increases, and when $N\rightarrow\infty$, it arrives at an asymptotic value determined by the decoherence rate $\gamma$ and the structure of the spin network.