We study the macroscopic realism (macrorealism) through the two- and three-time Leggett-Garg inequalities (LGIs) in a two-interacting-qubits system. The two qubits are coupled either with two bosonic (thermal or photonic) baths or fermionic (electronic) baths. We study both how the equilibrium and nonequilibrium environments influence the LGIs. One way to characterize the nonequilibrium condition is by the temperature difference (for the bosonic bath) or the chemical potential difference (for the fermionic bath). We also study the heat or particle current and the entropy production rate generated by the nonequilibrium environments. Analytical forms of LGIs and the maximal value of LGIs based on the quantum master equation beyond the secular approximation are derived. The LGI functions and the corresponding maximal value have separated contributions, the part describing the coherent evolution and the part describing the coupling between the system and environments. The environment-coupling part can be from the equilibrium environment or the nonequilibrium environment. The nonequilibrium dynamics is quantified by the Bloch-Redfield equation which is beyond the Lindblad form. We found that the nonequilibriumness quantified by the temperature difference or the chemical potential difference can lead to the LGIs' violations or the increase of the maximal value of LGIs, restoring the quantum nature from certain equilibrium cases where LGIs are preserved. The corresponding nonequilibrium thermodynamic cost is quantified by the nonzero entropy production rate. The violation enhancement increases with the increase of the entropy production rate under certain nonequilibrium conditions. Therefore, the LGIs' violation enhancement can be realized by the thermodynamic nonequilibrium cost. Our results shed light on the nature of the macrorealism and the relationship between the nonequilibriumness and the quantum temporal correlation. Our finding of the nonequilibrium promoted LGIs' violations suggests a new strategy for the design of quantum information processing and quantum computational devices to maintain the quantum nature and quantum correlations for long.
We study the macroscopic realism (macrorealism) through the two- and three-time Leggett-Garg inequalities (LGIs) in a two-interacting-qubits system. The two qubits are coupled either with two bosonic (thermal or photonic) baths or fermionic (electronic) baths. We study both how the equilibrium and nonequilibrium environments influence the LGIs. One way to characterize the nonequilibrium condition is by the temperature difference (for the bosonic bath) or the chemical potential difference (for the fermionic bath). We also study the heat or particle current and the entropy production rate generated by the nonequilibrium environments. Analytical forms of LGIs and the maximal value of LGIs based on the quantum master equation beyond the secular approximation are derived. The LGI functions and the corresponding maximal value have separated contributions, the part describing the coherent evolution and the part describing the coupling between the system and environments. The environment-coupling part can be from the equilibrium environment or the nonequilibrium environment. The nonequilibrium dynamics is quantified by the Bloch-Redfield equation which is beyond the Lindblad form. We found that the nonequilibriumness quantified by the temperature difference or the chemical potential difference can lead to the LGIs' violations or the increase of the maximal value of LGIs, restoring the quantum nature from certain equilibrium cases where LGIs are preserved. The corresponding nonequilibrium thermodynamic cost is quantified by the nonzero entropy production rate. The violation enhancement increases with the increase of the entropy production rate under certain nonequilibrium conditions. Therefore, the LGIs' violation enhancement can be realized by the thermodynamic nonequilibrium cost. Our results shed light on the nature of the macrorealism and the relationship between the nonequilibriumness and the quantum temporal correlation. Our finding of the nonequilibrium promoted LGIs' violations suggests a new strategy for the design of quantum information processing and quantum computational devices to maintain the quantum nature and quantum correlations for long.
We study macroscopic realism through the Leggett-Garg inequalities (LGI) in two interacting qubit system. The two qubits are coupled either with two Bosonic (thermal and photonic) baths or Fermionic (electronic) baths. We study both how the equilibrium and nonequilibrium environments influence the LGI. One way to characterize the nonequilibrium condition is by the different temperatures (for the Bosonic baths) or the different chemical potentials (for the Fermionic baths). We also study the heat or particle current and the entropy production rate generated by the nonequilibrium environments. Analytical forms of the LGI and the maximal values of LGI based on the quantum master equation beyond secular approximation are derived. The LGI function and its maximal value have separated contributions, the part describing the coherent evolution and the part describing the coupling between the system and environments. The environment coupling part can be from equilibrium environment or nonequilibrium environment. The nonequilibrium dynamics is quantified by the Bloch-Redfield equation which is beyond Lindblad form. We found that the nonequilibriumness quantified by the temperature difference or chemical potential difference can lead to the LGI violation or the increase of the maximal value of LGI, restoring the quantum nature from certain equilibrium cases where LGI is preserved which gives rise to classical realism. The corresponding nonequilibrium thermodynamic cost is quantified by the nonzero entropy production rate. The LGI violation enhancement increases with the increase of the entropy production rate under certain nonequilibrium conditions. Our finding of nonequilibrium promoted LGI violation suggests a new strategy for the design of quantum information processing and quantum computational devices to maintain the quantum nature and quantum correlations for long.
We investigate both analytically and numerically violations of a Leggett-Garg inequality (LGI) for a composite quantum system in contact with two separate reservoirs at different temperatures. Remarkably we find that LGI violations can be enhanced when a heat current is established at low temperatures in a steady-state regime. Based on a Kraus operator decomposition of the nonunitary evolution for a system formed by two interacting spins or quantum bits, we provide analytical support for power-law relations between dissipation strength and mean temperature in the borderlines separating parameter regions where nonequilibrium conditions affect differently the maximal LGI violation. Furthermore, a correspondence between spatial and temporal correlation inequalities is shown to persist even in such nonequilibrium thermal settings.
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.
In 1985, Leggett and Garg formulated a class of inequalities for testing the compatibility between macrorealism and quantum mechanics. In this paper, we point out that, based on the same assumptions of macrorealism that are used to derive Leggett-Garg inequalities (LGIs), there is a scope of formulating another class of inequalities different from the standard LGIs. By considering the three-time measurement scenario in a dichotomic system, we first propose an interesting variant of the standard LGIs and show that its quantum violation is larger than the standard LGIs. By extending this formulation to the n-time measurement scenario, we found that the quantum violations of variants of the LGIs for a qubit system increase with n, and, for a sufficiently large n, an algebraic maximum can be reached. We then compare the violations of the standard and variants of the LGIs in an unsharp measurement scenario and show that, for any arbitrary n, the violation of the latter is more robust to unsharpness than the former. Furthermore, we examine the relation between the quantum violations of the variants of the LGIs and an another formulation macrorealism, known as no-signaling in time conditions.
In this paper, we have studied the Shannon "entropic" nonequilibrium temperature (NET) of quantum Brownian systems. The Brownian particle is attached to either a bosonic or fermionic bath. Based on the Fokker-Planck description of the c-number quantum Langevin equation, we have calculated entropy production, NET, and their bounds. Entropy production (EP), the upper bound of entropy production (UBEP), and the deviation of the UBEP from EP monotonically decrease as functions of time to equilibrium value for both of the thermal baths. The deviation decreases with increase of temperature of the bosonic thermal bath, but it becomes larger as the temperature of the fermionic bath grows. We also observe that nonequilibrium temperature and its lower bound monotonically increase to equilibrium value with the progression of time. But their difference as a function of time shows an optimum behavior in most cases. Finally, we have observed that at long time, the entropic temperature (for a bosonic thermal bath) first increases nonlinearly as a function of thermodynamic temperature (TT) and, if the TT is appreciably large, then it grows linearly. But for the fermionic thermal bath, the entropic temperature decreases monotonically as a nonlinear function of thermodynamic temperature to zero value.
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.