Influence of environment on quantum correlations in two-spin systems with dipole-dipole interactions
G. A. Bochkin, E. B. Fel'dman, E. I. Kuznetsova, E. I. Shipulya
TL;DR
This paper investigates how environmental dephasing affects quantum correlations in a dipolar-coupled two-qubit system by solving the Lindblad master equation analytically. It yields an $X$-state density matrix $\rho_X(t)$ and provides closed-form expressions for entanglement (concurrence) and quantum discord, revealing that entanglement survives only below a finite temperature (e.g., $T \lesssim 27$ mK for $\beta=1.5$ and $\omega_0 = 2\pi \cdot 500$ MHz) while discord remains present at finite temperatures and decays more gradually with the relaxation rate $g$. The results show discord's greater robustness to dephasing compared with entanglement in open dipolar spin systems, and they establish an analytic framework that can be extended to more spins and experimental contexts such as NMR-based quantum information processing. Overall, the work provides a clear link between environmental parameters and the resilience of quantum correlations in open two-qubit dipolar systems.
Abstract
An influence of environment on quantum correlations (entanglement and quantum discord) is studied in a two-spin-1/2 system with dipole-dipole interactions on the basis of Lindblad equation. We consider the simplest case when the environment causes only dephasing of system spins. The dependencies of entanglement and the quantum discord on the relaxation rate are obtained. We compare the influence of the environment on entanglement and quantum discord.