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International Journal of Theoretical Physics

Steady-State Discord Between Two Qubits Coupled Collectively to a Thermal Reservoir

Xiang-Ping Liao, Jianshu Fang, Mao-Fa Fang, Zhong Hua Huang

Published Mar 24, 2011• 5 citations
Publisher
DOI
10.1007/s10773-011-0759-1

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A quantum thermal diode is designed based on three pairwise coupled qubits, two connected to a common reservoir and the other to an independent reservoir. It is found that the internal couplings between qubits can enhance heat currents. If the two identical qubits uniformly couple with the common reservoir, the crossing dissipation will occur, leading to the initial-state-dependent steady state, which can be decomposed into the mixture of two particular steady states: the heat-conducting state generating maximum heat current and the heat-resisting state not transporting heat. However, the rectification factor doesn't depend on the initial state. In particular, we find that neither quantum entanglement nor quantum discord is present in the steady state, but the pure classical correlation shows a remarkably consistent behavior as the heat rectification factor, which reveals the vital role of classical correlation in the system.
ABSTRACT We study the steady‐state quantum Fisher information (QFI) and several quantum resources entanglement, quantum coherence, and quantum discord for a pair of coupled qubits interacting with either bosonic or fermionic reservoirs. Using the Bloch–Redfield master equation beyond the secular approximation, we derive analytical expressions for the steady‐state density matrix and analyze how equilibrium and nonequilibrium conditions shape the resulting quantum correlations. In thermal equilibrium, the quantum resources display distinct behaviors depending on the bath statistics, with fermionic reservoirs enabling stronger stationary correlations due to particle‐exchange processes. Under nonequilibrium driving, generated either by a temperature imbalance or by a chemical potential difference, the system develops steady‐state coherence and enhanced discord, while entanglement and QFI exhibit non‐monotonic dependence governed by the interplay between coherence generation and population mixing. Our results identify the regimes in which steady‐state metrological performance can be optimized, and they provide general guidelines for enhancing quantum correlations in dissipative two‐qubit platforms.
Coupling of a quantum battery (QB) to two thermal reservoirs brings it to a nonequilibrium steady-state (NESS). In this situation, although, the QB can be charged through the NESS heat current, no work may be extracted from it through unitary cyclic processes. We exemplify this statement by studying the two- and three-qubit XXZXXZXXZ spin-chain QBs coupled weakly to two different thermal reservoirs in a symmetric configuration wherein each end of chain interacts with an individual reservoir. We show that the work can be extracted at positive temperature bias when two ends of a XXZXXZXXZ chain are collectively coupled to the hot reservoir.