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

Scientific Reports

Quantum violation of LGI under an energy constraint for different scenarios systems

Yuxia Zhang, Xiangguan Tan, Tianhui Qiu

Published Aug 2, 2023• 4 citations
Publisher

Abstract

In this paper, we consider a qubit in four scenarios: with drive, without drive, and in the presence of dissipation and dephasing, to investigate the quantum violation of the Leggett-Garg inequality (LGI) in an energy constraint. In the case of the energy constraint, we find that under the coarsening measurement in reference and final resolution, the quantum violation of the LGI for the pure qubit is the most robust; on the other hand, the quantum violation of the LGI for the dephasing qubit is the most vulnerable, and the quantum violation of the LGI for driven qubit lies between that of pure qubit and dissipation qubit. Under the coarsening of measurement temporal reference, the quantum violation of the LGI for the pure qubit is more robust than that of the qubit with driven. Moreover, in the case of a qubit that is subjected to driving and is in the presence of dissipation and dephasing, the robustness of quantum violations of the LGI for these scenario systems will become vulnerable, with the driven intensity and the rate of spontaneous emission increasing, respectively, for coarsening measurement both in reference and in final resolution. In addition, in the energy constraint and the projective measurement, the LGI can attain its maximum violation value, 1.5, for the coherent dynamics; while for drive, dissipative and dephasing qubits, the LGI cannot attain the value of 1.5. For systems in the presence of dissipation and dephasing, we find that in the energy constraint, the robustness of the coarsening measurement in final resolution exhibits more vulnerable than that of the coarsening measurement in reference. And for systems with drive and without drive, the robustness of the coarsening measurement in temporal reference is the most robust, and the robustness of the coarsening of measurement final measurement resolution is the most vulnerable.

DOI
10.1038/s41598-023-39612-6

Related papers

Comparing the quantum witness, the entropic Leggett–Garg inequality and the NCGD

Xiangguan Tan, Yuxia Zhang, Tianhui Qiu

In this paper, we investigate the violation of the quantum witness, the entropic Leggett-Garg inequality (LGI) and the no-coherence-generating-and-detecting (NCGD) dynamics, under projective and coarsening measurements. We consider a qubit in the three scenarios: coherent dynamics, in the presence of dissipation, and in the presence of dephasing. For the pure qubit, we find that in the case of the projective measurement, the non-violation conditions of the quantum witness and the NCGD are the same; while the non-violation conditions of the entropic LGI and the quantum witness do not contain each other, i.e., a suitable conjunction of the quantum witness and the entropic LGI may be better for testing macrorealism. Also, for the pure qubit with coarsening measurement similar results can be obtained. For the dissipative qubit with projective measurement, the quantum witness and the NCGD can be both violated for a wider parameter regime than the entropic LGI. For the dissipative qubit with coarsening measurement, the violation of the NCGD is the most robust compared to the quantum witness and the entropic LGI. For the dephasing qubit with projective and coarsening measurements, the relationship among the quantum witness, the entropic LGI and the NCGD is similar to that of the pure qubit. In addition, we find that for pure, dissipative and dephasing qubits, the robustness of the coarsening measurement in final resolution is more vulnerable than that of the coarsening measurement in reference for the entropic LGI.

Scientific Reports•May 2, 2024•1 citation

Canonical Leggett-Garg inequality: Nonclassicality of temporal quantum correlations under energy constraint

Titas Chanda, Tamoghna Das, Shiladitya Mal +2 more

Nonclassicality of temporal correlations pertaining to noncommutative sequential measurements is defined through the violation of macrorealistic inequalities, known as Leggett-Garg inequalities (LGI). We investigate the energy cost of the process associated with the Leggett-Garg test in the context of noiseless and Markovian noise for arbitrary initial states. We prove that in noiseless and in certain noisy scenarios, the maximal violations of LGI under the energy constraint occurs when the average energy of the process is equal to the negative of the energy of the initial state. Such a dependence of LGI on the choice of the initial state is not seen in the unconstrained case. Moreover, we find that in the presence of a moderate amount of Markovian noise, the amount of violation of LGI remains almost unaltered with a suitable choice of the evolution and dephasing operators in the neighborhood of the maximal violation line, thereby showing the robustness of temporal correlations under environmental effects.

arXiv:1805.04665•Physical Review A•Aug 29, 2018•15 citations

Probing nonclassicality under dissipation

Md. Manirul Ali, Po‐Wen Chen

Abstract We investigate the nonclassicality of an open quantum system using Leggett–Garg inequalities (LGI) which test the correlations of a single system measured at different times. Violation of LGI implies nonclassical behavior of the open system. We investigate the violation of the Leggett–Garg inequality for a two level system (qubit) spontaneously decaying under a general non-Markovian dissipative environment. A robust nonclassical behavior is shown through the violation of LGI in the non-Markovian regime of the environment. Our results are exact as we have evaluated the two-time correlation functions exactly without using quantum regression theorem. We probe quantum signatures of the open system through the exact dynamics of Leggett–Garg inequalities for a wide range of system-environment parameters beyond Born–Markov regime.

Journal of Physics A Mathematical and Theoretical•Sep 12, 2017•4 citations

Quantum violation of variants of Leggett-Garg inequalities up to the algebraic maximum for a qubit system

A. K. Pan, Md Qutubuddin, Swati Kumari

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.

arXiv:1806.01219•Physical Review A•Dec 19, 2018•18 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

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
In this paper, we consider a qubit in four scenarios: with drive, without drive, and in the presence of dissipation and dephasing, to investigate the quantum violation of the Leggett-Garg inequality (LGI) in an energy constraint. In the case of the energy constraint, we find that under the coarsening measurement in reference and final resolution, the quantum violation of the LGI for the pure qubit is the most robust; on the other hand, the quantum violation of the LGI for the dephasing qubit is the most vulnerable, and the quantum violation of the LGI for driven qubit lies between that of pure qubit and dissipation qubit. Under the coarsening of measurement temporal reference, the quantum violation of the LGI for the pure qubit is more robust than that of the qubit with driven. Moreover, in the case of a qubit that is subjected to driving and is in the presence of dissipation and dephasing, the robustness of quantum violations of the LGI for these scenario systems will become vulnerable, with the driven intensity and the rate of spontaneous emission increasing, respectively, for coarsening measurement both in reference and in final resolution. In addition, in the energy constraint and the projective measurement, the LGI can attain its maximum violation value, 1.5, for the coherent dynamics; while for drive, dissipative and dephasing qubits, the LGI cannot attain the value of 1.5. For systems in the presence of dissipation and dephasing, we find that in the energy constraint, the robustness of the coarsening measurement in final resolution exhibits more vulnerable than that of the coarsening measurement in reference. And for systems with drive and without drive, the robustness of the coarsening measurement in temporal reference is the most robust, and the robustness of the coarsening of measurement final measurement resolution is the most vulnerable.
In this paper, we investigate the violation of the quantum witness, the entropic Leggett-Garg inequality (LGI) and the no-coherence-generating-and-detecting (NCGD) dynamics, under projective and coarsening measurements. We consider a qubit in the three scenarios: coherent dynamics, in the presence of dissipation, and in the presence of dephasing. For the pure qubit, we find that in the case of the projective measurement, the non-violation conditions of the quantum witness and the NCGD are the same; while the non-violation conditions of the entropic LGI and the quantum witness do not contain each other, i.e., a suitable conjunction of the quantum witness and the entropic LGI may be better for testing macrorealism. Also, for the pure qubit with coarsening measurement similar results can be obtained. For the dissipative qubit with projective measurement, the quantum witness and the NCGD can be both violated for a wider parameter regime than the entropic LGI. For the dissipative qubit with coarsening measurement, the violation of the NCGD is the most robust compared to the quantum witness and the entropic LGI. For the dephasing qubit with projective and coarsening measurements, the relationship among the quantum witness, the entropic LGI and the NCGD is similar to that of the pure qubit. In addition, we find that for pure, dissipative and dephasing qubits, the robustness of the coarsening measurement in final resolution is more vulnerable than that of the coarsening measurement in reference for the entropic LGI.
Nonclassicality of temporal correlations pertaining to noncommutative sequential measurements is defined through the violation of macrorealistic inequalities, known as Leggett-Garg inequalities (LGI). We investigate the energy cost of the process associated with the Leggett-Garg test in the context of noiseless and Markovian noise for arbitrary initial states. We prove that in noiseless and in certain noisy scenarios, the maximal violations of LGI under the energy constraint occurs when the average energy of the process is equal to the negative of the energy of the initial state. Such a dependence of LGI on the choice of the initial state is not seen in the unconstrained case. Moreover, we find that in the presence of a moderate amount of Markovian noise, the amount of violation of LGI remains almost unaltered with a suitable choice of the evolution and dephasing operators in the neighborhood of the maximal violation line, thereby showing the robustness of temporal correlations under environmental effects.
Abstract We investigate the nonclassicality of an open quantum system using Leggett–Garg inequalities (LGI) which test the correlations of a single system measured at different times. Violation of LGI implies nonclassical behavior of the open system. We investigate the violation of the Leggett–Garg inequality for a two level system (qubit) spontaneously decaying under a general non-Markovian dissipative environment. A robust nonclassical behavior is shown through the violation of LGI in the non-Markovian regime of the environment. Our results are exact as we have evaluated the two-time correlation functions exactly without using quantum regression theorem. We probe quantum signatures of the open system through the exact dynamics of Leggett–Garg inequalities for a wide range of system-environment parameters beyond Born–Markov regime.
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 nnn-time measurement scenario, we found that the quantum violations of variants of the LGIs for a qubit system increase with nnn, and, for a sufficiently large nnn, 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 nnn, 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.
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.
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.