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:1912.12030 · Journal of Physics A Mathematical and Theoretical

P T symmetric evolution, coherence and violation of Leggett–Garg inequalities

Javid Naikoo, Swati Kumari, Subhashish Banerjee, A. K. Pan

Published May 26, 2021• 12 citations
arXivHTMLPDF

Abstract

Abstract We report an unusual buildup of the quantum coherence in a qubit subjected to non-Hermitian evolution generated by a parity-time ( PT ) symmetric Hamiltonian, which is reinterpreted as a Hermitian system in a higher dimensional space using Naimark dilation. The coherence is found to be maximum about the exceptional points (EPs), i.e. the points of coalescence of the eigenvalues as well as the eigenvectors. The nontrivial physics about EPs has been observed in various systems, particularly in photonic systems. As a consequence of enhancement in coherence, the various formulations of Leggett–Garg inequality tests show maximal violation about the EPs.

DOI
10.1088/1751-8121/ac0546

Related papers

Maximal coherent behavior about exceptional points in a $\mathcal{PT}$ symmetric qubit

Javid Naikoo, Swati Kumari, A. K. Pan +1 more

We report an unusual buildup of the quantum coherence in a qubit subjected to non-Hermitian evolution generated by a Parity-Time ($\mathcal{PT}$) symmetric Hamiltonian. The coherence is found to be maximum about the exceptional points (EPs), i.e., the points of coalescence of the eigenvalues as well as the eigenvectors. The nontrivial physics about EPs has been observed in various systems, particularly in photonic systems. As a consequence of enhance in coherence, the various formulations of Leggett-Garg inequality tests show maximal prediction about the EPs.

•Dec 27, 2019•0 citations

Quantum information dynamics in a high-dimensional parity-time-symmetric system

Zhihao Bian, Lei Xiao, Kunkun Wang +5 more

Non-Hermitian systems with parity-time ($\mathcal{PT}$) symmetry give rise to exceptional points (EPs) with exceptional properties that arise due to the coalescence of eigenvectors. Such systems have been extensively explored in the classical domain, where second- or higher-order EPs have been proposed or realized. In contrast, quantum information studies of $\mathcal{PT}$-symmetric systems have been confined to systems with a two-dimensional Hilbert space. Here, by using a single-photon interferometry setup, we simulate the quantum dynamics of a four-dimensional $\mathcal{PT}$-symmetric system across a fourth-order exceptional point. By tracking the coherent, nonunitary evolution of the density matrix of the system in $\mathcal{PT}$-symmetry unbroken and broken regions, we observe the entropy dynamics for both the entire system, and the gain and loss subsystems. Our setup is scalable to the higher-dimensional $\mathcal{PT}$-symmetric systems, and our results point towards the rich dynamics and critical properties.

arXiv:2102.06721•Physical Review A•Sep 16, 2020•29 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

Leggett-Garg inequalities and temporal correlations for a qubit under PT -symmetric dynamics

H. S. Karthik, Akshata Shenoy H., A. R. Usha Devi

Macrorealistic description governing the classical realm is known to get uprooted in the quantum domain. The Leggett-Garg inequality [A. J. Leggett and A. Garg, Phys. Rev. Lett. 54, 857 (1985)] proposes to probe the macrorealistic limit emerging from the quantum scenario. It places a bound on the linear combinations of temporal correlations of observables measured sequentially at different time intervals. Violation of the Leggett-Garg inequality, up to the so-called temporal Tsirelson bound (TTB), has been realized in the quantum domain. It is important to understand whether quantum theory permits larger violation beyond the TTB and up to the algebraic maximum value of the Leggett-Garg inequality. To this end, it has been shown [C. Budroni and C. Emary, Phys. Rev. Lett. 113, 050401 (2014)] that a three-term Leggett-Garg inequality can be violated beyond the TTB $3/2$ in the time evolution of $N>2$ level quantum systems by choosing suitable measurement schemes and state-update rules. Furthermore, it is revealed that the algebraic maximum value 3 can be realized in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$. Their measurement scheme rules out violation of the Leggett-Garg inequality beyond the TTB by a qubit. Being genuinely quantum in nature, we ask whether such enhanced violation of the Leggett-Garg inequality could be witnessed in a qubit itself. Here, we show that a qubit undergoing time evolution generated by a non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian indeed violates the three-term Leggett-Garg inequality beyond the TTB and up to its algebraic maximum value 3.

arXiv:1907.02879•Physical Review A•Mar 17, 2021•13 citations

Temporal correlation beyond quantum bounds in non-Hermitian PT- symmetric dynamics of a two level system

Anant Vijay Varma, Ipsika Mohanty, Sourin Das

Abstract We study the dynamics of a non-Hermitian PT- symmetric Hamiltonian of a two level system (TLS) which has real eigenvalues. Within the framework of Hermitian quantum mechanics, it is known that maximal violation of Leggett–Garg inequality (LGI) is bounded by K 3 = 3/2 (Luder’s bound). We show that this absolute bound can be evaded when dynamics is governed by non-Hermitian PT- symmetric Hamiltonians with real eigenvalues. Moreover, the extent of violation can be optimized to asymptotically approach the algebraic maximum of K 3 max = 3 , which is otherwise observed for Hermitian Hamiltonian with infinite dimensional Hilbert space. The extreme violation of LGI is shown to be directly related to the two basic ingredients: (i) the Bloch equation for the TLS having a non-linear terms which allow for accelerated dynamics of states on the Bloch sphere exceeding all known quantum speed limits of state evolution; and (ii) quantum trajectory of states lie on a great circle (geodesic path) on the Bloch sphere at all times. We demonstrate that such extreme temporal correlation of TLS can be simulated in realistic system by embedding the TLS into a higher dimensional Hilbert space such that the composite system obeys unitary dynamics. Specifically we show that a four dimensional embedding of non-Hermitian PT- symmetric TLS is enough to host K 3 → 3 limit. We also discuss the effect of random noise on our results. Finally we conclude with a comparative study of our results with existing experimental realization of embedding.

arXiv:1907.13400•Journal of Physics A Mathematical and Theoretical•Jan 21, 2021•10 citations

Parity-time-symmetric two-qubit system: entanglement and sensing

J. Zhang, Y. L. Zhou, Yunlan Zuo +3 more

In this paper we study exceptional-point (EP) effects and quantum sensing in a parity-time (PT)-symmetric two-qubit system with the Ising-type interaction. We explore EP properties of the system by analyzing degeneracy of energy eigenvalues or entanglement of eigenstates. We investigate entanglement dynamics of the two qubits in detail. In particular, we demonstrate that the system can create the steady-state entanglement in the PT-broken phase and collapse-revival phenomenon of entanglement in the PT-symmetric phase during the long-time evolution. We show that entanglement can be generated more quickly than the corresponding Hermitian system. Finally, we prove that the sensitivity of eigenstate quantum sensing for the parameters exhibits the remarkable enharncement at EPs, and propose a quantum-coherence measurement to witness the existence of EPs.

arXiv:2305.19034•May 30, 2023•1 citation
Abstract We report an unusual buildup of the quantum coherence in a qubit subjected to non-Hermitian evolution generated by a parity-time ( PT ) symmetric Hamiltonian, which is reinterpreted as a Hermitian system in a higher dimensional space using Naimark dilation. The coherence is found to be maximum about the exceptional points (EPs), i.e. the points of coalescence of the eigenvalues as well as the eigenvectors. The nontrivial physics about EPs has been observed in various systems, particularly in photonic systems. As a consequence of enhancement in coherence, the various formulations of Leggett–Garg inequality tests show maximal violation about the EPs.
Maximal coherent behavior about exceptional points in a PT\mathcal{PT}PT symmetric qubit
We report an unusual buildup of the quantum coherence in a qubit subjected to non-Hermitian evolution generated by a Parity-Time (PT\mathcal{PT}PT) symmetric Hamiltonian. The coherence is found to be maximum about the exceptional points (EPs), i.e., the points of coalescence of the eigenvalues as well as the eigenvectors. The nontrivial physics about EPs has been observed in various systems, particularly in photonic systems. As a consequence of enhance in coherence, the various formulations of Leggett-Garg inequality tests show maximal prediction about the EPs.
Non-Hermitian systems with parity-time (PT\mathcal{PT}PT) symmetry give rise to exceptional points (EPs) with exceptional properties that arise due to the coalescence of eigenvectors. Such systems have been extensively explored in the classical domain, where second- or higher-order EPs have been proposed or realized. In contrast, quantum information studies of PT\mathcal{PT}PT-symmetric systems have been confined to systems with a two-dimensional Hilbert space. Here, by using a single-photon interferometry setup, we simulate the quantum dynamics of a four-dimensional PT\mathcal{PT}PT-symmetric system across a fourth-order exceptional point. By tracking the coherent, nonunitary evolution of the density matrix of the system in PT\mathcal{PT}PT-symmetry unbroken and broken regions, we observe the entropy dynamics for both the entire system, and the gain and loss subsystems. Our setup is scalable to the higher-dimensional PT\mathcal{PT}PT-symmetric systems, and our results point towards the rich dynamics and critical properties.
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.
Macrorealistic description governing the classical realm is known to get uprooted in the quantum domain. The Leggett-Garg inequality [A. J. Leggett and A. Garg, Phys. Rev. Lett. 54, 857 (1985)] proposes to probe the macrorealistic limit emerging from the quantum scenario. It places a bound on the linear combinations of temporal correlations of observables measured sequentially at different time intervals. Violation of the Leggett-Garg inequality, up to the so-called temporal Tsirelson bound (TTB), has been realized in the quantum domain. It is important to understand whether quantum theory permits larger violation beyond the TTB and up to the algebraic maximum value of the Leggett-Garg inequality. To this end, it has been shown [C. Budroni and C. Emary, Phys. Rev. Lett. 113, 050401 (2014)] that a three-term Leggett-Garg inequality can be violated beyond the TTB 3/23/23/2 in the time evolution of N>2N>2N>2 level quantum systems by choosing suitable measurement schemes and state-update rules. Furthermore, it is revealed that the algebraic maximum value 3 can be realized in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$. Their measurement scheme rules out violation of the Leggett-Garg inequality beyond the TTB by a qubit. Being genuinely quantum in nature, we ask whether such enhanced violation of the Leggett-Garg inequality could be witnessed in a qubit itself. Here, we show that a qubit undergoing time evolution generated by a non-Hermitian PT\mathcal{P}\mathcal{T}PT-symmetric Hamiltonian indeed violates the three-term Leggett-Garg inequality beyond the TTB and up to its algebraic maximum value 3.
Abstract We study the dynamics of a non-Hermitian PT- symmetric Hamiltonian of a two level system (TLS) which has real eigenvalues. Within the framework of Hermitian quantum mechanics, it is known that maximal violation of Leggett–Garg inequality (LGI) is bounded by K 3 = 3/2 (Luder’s bound). We show that this absolute bound can be evaded when dynamics is governed by non-Hermitian PT- symmetric Hamiltonians with real eigenvalues. Moreover, the extent of violation can be optimized to asymptotically approach the algebraic maximum of K 3 max = 3 , which is otherwise observed for Hermitian Hamiltonian with infinite dimensional Hilbert space. The extreme violation of LGI is shown to be directly related to the two basic ingredients: (i) the Bloch equation for the TLS having a non-linear terms which allow for accelerated dynamics of states on the Bloch sphere exceeding all known quantum speed limits of state evolution; and (ii) quantum trajectory of states lie on a great circle (geodesic path) on the Bloch sphere at all times. We demonstrate that such extreme temporal correlation of TLS can be simulated in realistic system by embedding the TLS into a higher dimensional Hilbert space such that the composite system obeys unitary dynamics. Specifically we show that a four dimensional embedding of non-Hermitian PT- symmetric TLS is enough to host K 3 → 3 limit. We also discuss the effect of random noise on our results. Finally we conclude with a comparative study of our results with existing experimental realization of embedding.
In this paper we study exceptional-point (EP) effects and quantum sensing in a parity-time (PT)-symmetric two-qubit system with the Ising-type interaction. We explore EP properties of the system by analyzing degeneracy of energy eigenvalues or entanglement of eigenstates. We investigate entanglement dynamics of the two qubits in detail. In particular, we demonstrate that the system can create the steady-state entanglement in the PT-broken phase and collapse-revival phenomenon of entanglement in the PT-symmetric phase during the long-time evolution. We show that entanglement can be generated more quickly than the corresponding Hermitian system. Finally, we prove that the sensitivity of eigenstate quantum sensing for the parameters exhibits the remarkable enharncement at EPs, and propose a quantum-coherence measurement to witness the existence of EPs.