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Annalen der Physik

Dissipative Quantum Systems: Reservoir‐Mediated Enhancement of Quantum Fisher Information and Non‐Classical Correlations

Nour-Eddine Abouelkhir, Safae Gaidi, Abdallah Slaoui, Rachid Ahl Laamara

Published Mar 1, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1002/andp.70190

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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.
We analytically and numerically investigate the steady-state entanglement and coherence of two coupled qubits, each interacting with a local boson or fermion reservoir, based on the Bloch-Redfield master equation beyond the secular approximation. We find that there is nonvanishing steady-state coherence in the nonequilibrium scenario, which grows monotonically with the nonequilibrium condition quantified by the temperature difference or chemical potential difference of the two baths. The steady-state entanglement, in general, is a nonmonotonic function of the nonequilibrium condition as well as the bath parameters in the equilibrium setting. We also discover that weak interqubit coupling and high base temperature or chemical potential of the baths can strongly suppress the steady-state entanglement and coherence, regardless of the strength of the nonequilibrium condition. On the other hand, the energy detuning of the two qubits, when used in a compensatory way with the nonequilibrium condition, can lead to significant enhancement of the steady-state entanglement in some parameter regimes. In addition, the qubits typically have a stronger steady-state entanglement when coupled to fermion baths exchanging particles with the system than boson baths exchanging energy with the system, under similar conditions. We also identify a close connection between the energy current flowing through the system and the steady-state coherence. Preliminary investigations suggest that these results are insensitive to the form of the reservoir spectral densities in the Markovian regime. Feasible experimental realization of measuring the steady-state entanglement and coherence is discussed for the coupled qubit system in nonequilibrium environments. Our findings offer some general guidelines for optimizing the steady-state entanglement and coherence in the coupled qubit system and may find potential applications in quantum information technology.
We study the steady-state entanglement and correlations of an open system comprising two coupled fermions in the equilibrium or nonequilibrium environments and distill the nonequilibrium contribution to the quantum correlations. We show that in the equilibrium condition, the steady-state quantum correlations exhibit nonmonotonic behavior, while in the nonequilibrium case, the monotonicity is determined by many parameters. The entanglement vanishes abruptly upon the increase of the temperature (bias) and chemical potential bias, and it witnesses a critical chemical potential above which the concurrence always remains positive. In the fermionic reservoirs, quantum correlations reach the maximal values when one chemical potential of the reservoirs matches the system frequency. We separate the quantum correlation generation due to the averaged effect from the pure nonequilibrium effect. In contrast with previous results, when the averaged effect is separated out, the nonequilibrium generation of quantum correlation shows a distinctive monotonic behavior. The difference between the large-tunneling regime with decaying correlations and the small-tunneling with increasing correlations is discussed. Near the boundary of the two regimes, the entanglement behavior is a mixture of two extremes, and it resurrects with the increase of chemical potential bias after its previous drop to zero.
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Quantum discord captures quantum correlations beyond entanglement and can remain finite even when the entanglement vanishes. We investigate the transient nonequilibrium dynamics and steady-state behavior of quantum discord and classical correlations in a double quantum dot (DQD) system coupled to fermionic reservoirs. By employing a quantum Langevin equation formalism, we obtain the exact reduced density matrix of the system, enabling a comprehensive analysis of its quantum and classical correlations under nonequilibrium conditions. The influence of system-reservoir coupling strength, spectral bandwidth, thermal bias, and varying initial state on both the transient dynamics and steady-state correlations is systematically analyzed. Quantum discord remains finite in the nonequilibrium steady state over a broad parameter range. Although thermal gradients reduce the overall magnitude of correlations, quantum discord persists and exhibits greater resilience. These results demonstrate that nonequilibrium electronic transport, together with the environmental spectral properties and reservoir asymmetry, provides an effective means of controlling nonclassical correlations in mesoscopic systems and establishes quantum discord as a robust hallmark of open fermionic quantum devices.
We investigate the non-monotonic temperature sensitivity of a coherently driven two-level quantum system coupled to an Ohmic phonon environment. By employing a unitary polaron transformation, we account for phonon-induced renormalization effects that go beyond the standard weak-coupling approximations. Our analysis reveals that the Quantum Fisher Information (QFI) exhibits a prominent peak at an intermediate system-environment coupling strength, identifying an optimal regime for thermal sensing. This behavior emerges from a fundamental competition between environment-induced dissipation enhancement and the exponential suppression of system parameters due to phonon dressing. We demonstrate that while thermometric precision vanishes in both the ultra-weak and strong coupling limits, a properly tuned nonequilibrium steady state can significantly enhance sensitivity. These results suggest that environmental interactions, often viewed as detrimental decoherence sources, can be engineered as a resource to optimize the performance of solid-state quantum thermometers.
This study investigates the thermodynamic behavior of a two-qubit quantum system, where each qubit is coupled to an independent thermal reservoir, either bosonic or fermionic. Using a master equation approach, we analyze both steady-state and time-dependent ergotropy to understand how different reservoir statistics affect work extraction. In bosonic environments, ergotropy consistently declines with increasing temperature due to thermal noise. In contrast, fermionic reservoirs exhibit more complex behavior, with ergotropy enhanced by particle transport under non-equilibrium conditions. Our results reveal a threshold-like sensitivity to the chemical potential configuration, leading to qualitatively distinct regimes of energy storage performance. Time-resolved analyses show that the system's approach to steady state varies depending on the type of reservoir and the coupling strength between qubits. These insights highlight how carefully engineered reservoir properties and non-equilibrium driving can be leveraged to optimize quantum battery performance.