Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1305.1323 · Physical Review A

Enhanced violation of a Leggett-Garg inequality under nonequilibrium thermal conditions

Juan Camilo Castillo, Ferney J. Rodríguez, Luis Quiroga

Published Aug 7, 2013• 17 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.88.022104

Related papers

The influence of equilibrium and nonequilibrium environments on the macroscopic realism through Leggett-Garg inequality

Kun Zhang, Wei Wu, Jin Wang

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.

•Jan 25, 2020•1 citation

Investigating Leggett-Garg inequality for a two level system under decoherence in a non-Markovian dephasing environment

Po‐Wen Chen, Md. Manirul Ali

Leggett-Garg inequalities (LGI) test the correlations of a single system measured at different times. Violation of LGI implies either the absence of a realistic description of the system or the impossibility of measuring the system without disturbing it. We investigate the violation of the Leggett-Garg inequality for a two level system under decoherence in a non-Markovian dephasing environment. We discuss the non-Markovian dynamics of the violation of LGI at zero temperature and also at finite temperature for different structured environments. An enhanced quantum coherence is shown through the violation of Leggett-Garg inequality in the strong non-Markovian regime of the environment.

Scientific Reports•Aug 22, 2014•21 citations

Influence of equilibrium and nonequilibrium environments on macroscopic realism through the Leggett-Garg inequalities

Kun Zhang, Wei Wu, Jin Wang

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.

arXiv:2001.09358•Physical Review A•May 22, 2020•12 citations

Experimental demonstration of enhanced violations of Leggett-Garg inequalities in a PT -symmetric trapped-ion qubit

Pengfei Lu, Xinxin Rao, Teng Liu +4 more

The Leggett-Garg inequality (LGI) delineates a boundary between quantum and classical systems. While the temporal quantum correlations represented by LGIs have been extensively investigated in the Hermitian domain, the exploration of LGIs under non-Hermitian conditions remains scarce. Theoretical conjectures posit that nonunitary dynamics could transcend the boundary of LGIs set by Hermitian quantum mechanics, yet its empirical validation is lacking. Here, we demonstrate the enhanced violation of LGIs in a non-Hermitian system of a parity-time ($\mathcal{PT}$)-symmetric trapped-ion qubit. The upper bounds of both the third-order parameter ${K}_{3}$ and fourth-order parameter ${K}_{4}$ increase with dissipation and can reach the maximum value when the system approaches the exceptional point, where ${K}_{3}={C}_{21}+{C}_{32}\ensuremath{-}{C}_{31}$ is comprising three two-time correlations and ${K}_{4}={C}_{21}+{C}_{32}+{C}_{43}\ensuremath{-}{C}_{41}$ is comprising four correlations. We also find that the lower bounds of ${K}_{3}$ and ${K}_{4}$ exhibit distinctive behaviors, where the lower bound of ${K}_{3}$ remains constant, but that of ${K}_{4}$ depends on the target states and measurement operators. These findings reveal a pronounced correlation between the dissipative nature of a quantum system and its temporal correlations.

arXiv:2309.06713•Physical Review A•Apr 8, 2024•12 citations

Comparison between the effects of Hamiltonian and Liouvillian exceptional points on the Leggett–Garg inequality and no-signaling-in-time conditions

Kun-Jie Zhou, Jian Zou, Bao-Ming Xu +1 more

Abstract In this paper, we investigate the effect of exceptional points (EPs) on the violation of Leggett–Garg inequality (LGI) and no-signaling-in-time (NSIT) conditions and compare the different effects between the Hamiltonian EP (HEP) and Liouvillian EP (LEP) on those violations. We consider an open system consisting of two coupled qubits and each qubit is contacted with a thermal bath at a different temperature. In the case of omitting quantum jumps, we find that the system exhibits a second-order HEP, which separates the parameter space into an overdamped regime and an underdamped regime. In this situation, the LGI and NSIT conditions can be violated in both regimes and not violated at the HEP. In the case of without omitting quantum jumps, we find that the system exhibits a third-order LEP, which also separates the parameter space into an overdamped regime and an underdamped regime. In this situation, the LGI can only be violated in the underdamped regime with large coupling strength between the qubits. Conversely, the NSIT conditions can be violated in both regimes, as well as at the LEP, except in the overdamped regime with small coupling strength between the qubits. Comparing the violations of the LGI and NSIT conditions with HEP and LEP, we find that the quantum jumps would reduce the generation of coherence, enhance the decoherence, and lead to narrower parameter regimes that the LGI and NSIT conditions can be violated. Furthermore, in both cases, the NSIT conditions can be violated in a wider parameter regime than the LGI.

Communications in Theoretical Physics•Feb 13, 2025•0 citations

Leggett-Garg inequality for qubits coupled to thermal environment

Marcin Łobejko, J. Łuczka, Jerzy Dajka

We study violation of the Leggett-Garg inequality for the correlator ${K}_{3}$ in two cases: (i) for a qubit weakly coupled to a thermal decohering (dissipative and/or dephasing) environment and (ii) for a pair of qubits with only one of them coupled to the environment. In the case of a single qubit, we identify conditions depending both on initial state preparation and a measurement protocol when violation of the ${K}_{3}$ inequality becomes dependent only on dephasing and independent of dissipation and temperature. In the case of two qubits, we have found the temperature-independent regime as well as the regime where all three components of the decoherence can control violation of the Leggett-Garg inequality.

Physical Review A•Apr 13, 2015•19 citations
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 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.
Leggett-Garg inequalities (LGI) test the correlations of a single system measured at different times. Violation of LGI implies either the absence of a realistic description of the system or the impossibility of measuring the system without disturbing it. We investigate the violation of the Leggett-Garg inequality for a two level system under decoherence in a non-Markovian dephasing environment. We discuss the non-Markovian dynamics of the violation of LGI at zero temperature and also at finite temperature for different structured environments. An enhanced quantum coherence is shown through the violation of Leggett-Garg inequality in the strong non-Markovian regime of the environment.
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.
The Leggett-Garg inequality (LGI) delineates a boundary between quantum and classical systems. While the temporal quantum correlations represented by LGIs have been extensively investigated in the Hermitian domain, the exploration of LGIs under non-Hermitian conditions remains scarce. Theoretical conjectures posit that nonunitary dynamics could transcend the boundary of LGIs set by Hermitian quantum mechanics, yet its empirical validation is lacking. Here, we demonstrate the enhanced violation of LGIs in a non-Hermitian system of a parity-time (PT\mathcal{PT}PT)-symmetric trapped-ion qubit. The upper bounds of both the third-order parameter K3{K}_{3}K3​ and fourth-order parameter K4{K}_{4}K4​ increase with dissipation and can reach the maximum value when the system approaches the exceptional point, where ${K}_{3}={C}_{21}+{C}_{32}\ensuremath{-}{C}_{31}$ is comprising three two-time correlations and ${K}_{4}={C}_{21}+{C}_{32}+{C}_{43}\ensuremath{-}{C}_{41}$ is comprising four correlations. We also find that the lower bounds of K3{K}_{3}K3​ and K4{K}_{4}K4​ exhibit distinctive behaviors, where the lower bound of K3{K}_{3}K3​ remains constant, but that of K4{K}_{4}K4​ depends on the target states and measurement operators. These findings reveal a pronounced correlation between the dissipative nature of a quantum system and its temporal correlations.
Abstract In this paper, we investigate the effect of exceptional points (EPs) on the violation of Leggett–Garg inequality (LGI) and no-signaling-in-time (NSIT) conditions and compare the different effects between the Hamiltonian EP (HEP) and Liouvillian EP (LEP) on those violations. We consider an open system consisting of two coupled qubits and each qubit is contacted with a thermal bath at a different temperature. In the case of omitting quantum jumps, we find that the system exhibits a second-order HEP, which separates the parameter space into an overdamped regime and an underdamped regime. In this situation, the LGI and NSIT conditions can be violated in both regimes and not violated at the HEP. In the case of without omitting quantum jumps, we find that the system exhibits a third-order LEP, which also separates the parameter space into an overdamped regime and an underdamped regime. In this situation, the LGI can only be violated in the underdamped regime with large coupling strength between the qubits. Conversely, the NSIT conditions can be violated in both regimes, as well as at the LEP, except in the overdamped regime with small coupling strength between the qubits. Comparing the violations of the LGI and NSIT conditions with HEP and LEP, we find that the quantum jumps would reduce the generation of coherence, enhance the decoherence, and lead to narrower parameter regimes that the LGI and NSIT conditions can be violated. Furthermore, in both cases, the NSIT conditions can be violated in a wider parameter regime than the LGI.
We study violation of the Leggett-Garg inequality for the correlator K3{K}_{3}K3​ in two cases: (i) for a qubit weakly coupled to a thermal decohering (dissipative and/or dephasing) environment and (ii) for a pair of qubits with only one of them coupled to the environment. In the case of a single qubit, we identify conditions depending both on initial state preparation and a measurement protocol when violation of the K3{K}_{3}K3​ inequality becomes dependent only on dephasing and independent of dissipation and temperature. In the case of two qubits, we have found the temperature-independent regime as well as the regime where all three components of the decoherence can control violation of the Leggett-Garg inequality.