Dynamics of tripartite correlations for three qubits in independent thermal reservoirs

TL;DR

This paper studies how temperature gradients between independent thermal reservoirs affect the robustness and dynamics of multipartite entanglement in three-qubit systems, revealing non-linear preservation effects and correlation sudden death phenomena.

Contribution

It provides an exact solution for the time evolution of tripartite entanglement in three-qubit systems coupled to thermal reservoirs with temperature gradients, highlighting novel robustness and decay behaviors.

Findings

Multipartite concurrence increases with temperature gradient but saturates at high gradients.

Multiple intervals of coherence preservation occur for large temperature gradients.

Correlation sudden death occurs for GHZ states at low temperatures, depending on reservoir spectral density.

Abstract

We investigate the dynamical evolution of multipartite entanglement in tripartite systems with three qubits present in independent thermal reservoirs, modelled as infinite set of quantum harmonic oscillators. We show that the presence of temperature gradient between reservoirs play a significant role in robustness of multipartite correlation against environmental decoherence. Considering a bilinear form of interaction Hamiltonian, an exact expression for time evolved density matrix is presented. Interestingly, it is observed that the preservation duration of genuine multipartite concurrence for GHZ class Werner state increases as the temperature gradient between reservoirs are increased. However, this increase is non-linear and the preservation duration is shown to saturate for large temperature gradients. It is also observed that, for large temperature gradient, there are multiple intervals in which coherence and consequently the tripartite negativity shows robustness (freezing of correlation) against the environmental decoherence for W class Werner states. For the common temperature case, we show that the genuine multipartite concurrence for the GHZ class Werner state decays irreversibly, and the state experiences correlation sudden death, with a rate dependent on spectral density of the reservoirs under consideration. For the Ohmic reservoirs at low temperature, we observe that the state retains initial multipartite correlation upto a characteristic time and then sharply decays to zero with a correlation sudden death. We further investigate the dynamics of tripartite negativity and $l_{1}$ norm of coherence in the W class Werner states, and show irreversible degradation in these correlations.