Coherence restoring in communication line via controlled interaction with environment

TL;DR

This paper tackles coherence restoration in quantum communication lines by exploiting time-dependent Lindblad dynamics that conserve excitation number. The authors formulate a universal state-restoring condition $\rho^{(R)}_{ij}(t_{\mathrm{reg}})=\lambda_{ij}\rho^{(S)}_{ij}(0)$ and solve for maximally robust $\lambda$ via regularized least squares in a short XXZ spin chain with environmental controls on an extended receiver. They analyze the $(0,1)$-excitation sector to restore the 1-order coherence matrix, and provide extensive numerical results for $N^{(S)}=2$ demonstrating that centrally-symmetric damping patterns and simple edges-center templates yield strong restoration, with equal-$\lambda$ variants achievable under a constraint $\lambda_{01}=\lambda_{10}$. The work shows that engineered environmental interaction can replace unitary receiver-side operations and yields insights for robust quantum state transfer and coherent control in spin networks.

Abstract

We consider the state-restoring protocol based on the controlled interaction of a linear chain with environment through the specially adjusted step-wise time dependent Lindblad operators. We show that the best restoring result (maximal scale factors in the restored state) corresponds to the symmetrical Lindblad equation. (0,1)-excitation dynamics is considered numerically, and restoring protocol for the 1-order coherence matrix is proposed for the case of the two-qubit sender (receiver). The state-restoring with equal scale factors is also considered reflecting the uniform scaling of the restored information.

Figures (4)

• Figure 1: The state restoring in the chain of $N=8$ qubits. (a) The transmission quality $\lambda$ (\ref{['lammaxEx']}) as function of the registration time-instant $\tau_\mathrm{reg}$. The ten best peaks are marked with the red bullets. (b) The distributions of damping rates $\{a^{\mathrm{(opt)}}_{kj}\}$ corresponding to the marked peaks of the transmission quality $\lambda$ (\ref{['lammaxEx']})
• Figure 2: The state restoring in the chain of $N=10$ qubits. (a) Transmission quality $\lambda$ (\ref{['lammaxEx']}) as a function of registration time-instant $\tau_\mathrm{reg}$. The ten best peaks are marked with the red bullets. (b) The centrally-symmetric distributions of damping rates $\gamma^{\mathrm{(opt)}}$ corresponding to the marked peaks of transmission quality $\lambda$ (\ref{['lammaxEx']}).
• Figure 3: The damping rate values $\gamma^{\mathrm{(opt)}}$ corresponding to the maximum value of the transmission quality $\lambda$ (\ref{['lammaxEx']}) for different chain lengths $N$ and "edges and center"-model, which is the simplest pattern of a damping rate distribution. The appropriate registration time instants are given in Table \ref{['tbl:lamndas-with-edges-and-center-pattern-by-length']} together with the transmission quality $\lambda$ and maximal absolute value of the $\lambda$-parameters $\lambda_\mathrm{max}$.
• Figure 4: State restoring in the chain of $N=10$ qubits with equal $\lambda$-parameters. (a) The transmission quality $\lambda$ (\ref{['single-lammaxEx']}) as a function of the registration time-instant $\tau_\mathrm{reg}$. Ten best peaks are marked with the red bullets. (b) The centrally-symmetric distributions of damping rates $\{a_{kj}^\mathrm{(opt)}\}$ corresponding to the marked peaks of the transmission quality $\lambda$ (\ref{['single-lammaxEx']})