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

Chinese Physics B

Quantum speed limit time of a non-Hermitian two-level system

Yanyi Wang, Mao-Fa Fang

Published Jan 16, 2020• 16 citations
Publisher

Abstract

We investigated the quantum speed limit time of a non-Hermitian two-level system for which gain and loss of energy or amplitude are present. Our results show that, with respect to two distinguishable states of the non-Hermitian system, the evolutionary time does not have a nonzero lower bound. The quantum evolution of the system can be effectively accelerated by adjusting the non-Hermitian parameter, as well as the quantum speed limit time can be arbitrarily small even be zero.

DOI
10.1088/1674-1056/ab6c45

Related papers

Quantum speed limit time of a qubit system with non-Hermitian detuning

Yanyi Wang, Mao-Fa Fang

We investigated the quantum speed limit time of a qubit system with non-Hermitian detuning. Our results show that, with respect to two distinguishable states of the non-Hermitian system, the evolutionary time does not have a nonzero lower bound. And the quantum evolution of the system can be effectively accelerated by adjusting the non-Hermitian detuning parameter, as well as the quantum speed limit time can be arbitrarily small even be zero.

arXiv:1810.09066•Oct 22, 2018•0 citations

A General Quantum Speed Limit for Non-Hermitian Systems

Zhanxi Wang, Xiaozhe Hao, X. X. Yi

The quantum speed limit (QSL) refers to the maximum speed of a quantum system to evolve from an initial state to its orthogonal states. The bound on the QSL for Hermitian systems, for example the Mandelstam-Tamm (MT) and Margolus-Levitin (ML) as well as Sun-Zheng(SZ) bound, was studied respectively from the perspectives of average value and variance of the system Hamiltonian as well as the geometry of the system. While the compactness of the MT-type, ML-type and SZ-type bounds has been examined well for Hermitian systems, a compact QSL for non-Hermitian systems has not been well studied. In this work, based on the biorthogonal basis theory we derive two distinct and tighter bounds on the QSL for non-Hermitian systems, which correspond to the MT and ML bounds for Hermitian systems. We show that the shortest evolution time corresponding to the two bounds of the non-Hermitian system can be attained by certain initial states, showing the compactness and tightness of our bounds. These initial states dubbed fastest initial states(FIS) are different from that in Hermitian systems. A bound close to QSL for non-FIS is presented and comparison of our bound with others in literature is performed. To illustrate our results, we present a minimal non-Hermitian system to show QSL, and the condition for the shortest evolution time is derived analytically using the present theory.

quant-pharXiv:2605.23250•May 25, 2026•0 citations

Generalised quantum speed limit for arbitrary time-continuous evolution

Dimpi Thakuria, Abhay Srivastav, Brij Mohan +2 more

Abstract The quantum speed limit describes how quickly a quantum system can evolve in time from an initial state to a final state under a given dynamics. Here, we derive a generalised quantum speed limit (GQSL) for arbitrary time-continuous evolution using the geometrical approach of quantum mechanics. The GQSL is applicable for quantum systems undergoing unitary, non-unitary, completely positive, non-completely positive and relativistic quantum dynamics. This reduces to the well known standard quantum speed limit (QSL), i.e. the Mandelstam-Tamm bound when the quantum system undergoes unitary time evolution. Using our formalism, we then obtain a quantum speed limit for non-Hermitian quantum systems. To illustrate our findings, we have estimated the quantum speed limit for a time-independent non-Hermitian system as well as for a time-dependent non-Hermitian system namely the Bethe-Lamb Hamiltonian for general two-level system.

arXiv:2207.04124•Journal of Physics A Mathematical and Theoretical•Dec 14, 2023•18 citations

Quantum Speed Limit Quantified by the Changing Rate of Phase

Shuning Sun, Yonggang Peng, Xianghong Hu +1 more

The quantum speed limit is important in determining the minimum evolution time of a quantum system, and thus is essential for quantum community. In this Letter, we derive a novel unified quantum speed limit bound for Hermitian and non-Hermitian quantum systems. The bound is quantified by the changing rate of phase of the quantum system, which represents the transmission mode of the quantum states over their evolution. The bound leads to further insights beyond the previous bounds on concrete evolution modes of the quantum system, such as horizontal or parallel transition or horizontal joining of the two quantum states in Hilbert space. The bound is linked to the feasibility of the evolutions of the state vectors, and provides a tighter upper bound. In addition, the generalized Margolus-Levitin bound is discussed.

Physical Review Letters•Aug 31, 2021•46 citations

Time scaling and quantum speed limit in non-Hermitian Hamiltonians

François Impens, F. M. D'Angelis, F. A. Pinheiro +1 more

We report on a time-scaling technique to enhance the performances of quantum control protocols in non-Hermitian systems. The considered time scaling involves no extra couplings and yields a significant enhancement of the quantum fidelity for a comparable amount of resources. We discuss the application of this technique to quantum-state transfers in two- and three-level open quantum systems. We derive the quantum speed limit in a system governed by a non-Hermitian Hamiltonian. Interestingly, we show that with an appropriate driving the time-scaling technique preserves the optimality of the quantum speed with respect to the quantum speed limit whereas reducing significantly the damping of the quantum-state norm.

arXiv:2106.05155•Physical Review A•Nov 24, 2021•27 citations

Unified entropies and quantum speed limits for nonunitary dynamics

Diego Paiva Pires

We discuss a class of quantum speed limits (QSLs) based on unified quantum ($\ensuremath{\alpha},\ensuremath{\mu}$)-entropy for nonunitary physical processes. The bounds depend on both the Schatten speed and the smallest eigenvalue of the evolved state and the two-parametric unified entropy. We specialize these results to quantum channels and non-Hermitian evolutions. In the first case, the QSL depends on the Kraus operators related to the quantum channel, while in the second case the speed limit is recast in terms of the non-Hermitian Hamiltonian. To illustrate these findings, we consider a single-qubit state evolving under the (i) amplitude damping channel and (ii) the nonunitary dynamics generated by a parity-time-reversal symmetric non-Hermitian Hamiltonian. The QSL is nonzero at earlier times, while it becomes loose as the smallest eigenvalue of the evolved state approaches zero. Furthermore, we investigate the interplay between unified entropies and speed limits for the reduced dynamics of quantum many-body systems. The unified entropy is upper bounded by the quantum fluctuations of the Hamiltonian of the system, while the QSL is nonzero when entanglement is created by the nonunitary evolution. Finally, we apply these results to the XXZ model and verify that the QSL asymptotically decreases as the system size increases. Our results find applications to nonequilibrium thermodynamics, quantum metrology, and equilibration of many-body systems.

arXiv:2204.06476•Physical Review A•Jul 5, 2022•12 citations
We investigated the quantum speed limit time of a non-Hermitian two-level system for which gain and loss of energy or amplitude are present. Our results show that, with respect to two distinguishable states of the non-Hermitian system, the evolutionary time does not have a nonzero lower bound. The quantum evolution of the system can be effectively accelerated by adjusting the non-Hermitian parameter, as well as the quantum speed limit time can be arbitrarily small even be zero.
The quantum speed limit (QSL) refers to the maximum speed of a quantum system to evolve from an initial state to its orthogonal states. The bound on the QSL for Hermitian systems, for example the Mandelstam-Tamm (MT) and Margolus-Levitin (ML) as well as Sun-Zheng(SZ) bound, was studied respectively from the perspectives of average value and variance of the system Hamiltonian as well as the geometry of the system. While the compactness of the MT-type, ML-type and SZ-type bounds has been examined well for Hermitian systems, a compact QSL for non-Hermitian systems has not been well studied. In this work, based on the biorthogonal basis theory we derive two distinct and tighter bounds on the QSL for non-Hermitian systems, which correspond to the MT and ML bounds for Hermitian systems. We show that the shortest evolution time corresponding to the two bounds of the non-Hermitian system can be attained by certain initial states, showing the compactness and tightness of our bounds. These initial states dubbed fastest initial states(FIS) are different from that in Hermitian systems. A bound close to QSL for non-FIS is presented and comparison of our bound with others in literature is performed. To illustrate our results, we present a minimal non-Hermitian system to show QSL, and the condition for the shortest evolution time is derived analytically using the present theory.
Abstract The quantum speed limit describes how quickly a quantum system can evolve in time from an initial state to a final state under a given dynamics. Here, we derive a generalised quantum speed limit (GQSL) for arbitrary time-continuous evolution using the geometrical approach of quantum mechanics. The GQSL is applicable for quantum systems undergoing unitary, non-unitary, completely positive, non-completely positive and relativistic quantum dynamics. This reduces to the well known standard quantum speed limit (QSL), i.e. the Mandelstam-Tamm bound when the quantum system undergoes unitary time evolution. Using our formalism, we then obtain a quantum speed limit for non-Hermitian quantum systems. To illustrate our findings, we have estimated the quantum speed limit for a time-independent non-Hermitian system as well as for a time-dependent non-Hermitian system namely the Bethe-Lamb Hamiltonian for general two-level system.
The quantum speed limit is important in determining the minimum evolution time of a quantum system, and thus is essential for quantum community. In this Letter, we derive a novel unified quantum speed limit bound for Hermitian and non-Hermitian quantum systems. The bound is quantified by the changing rate of phase of the quantum system, which represents the transmission mode of the quantum states over their evolution. The bound leads to further insights beyond the previous bounds on concrete evolution modes of the quantum system, such as horizontal or parallel transition or horizontal joining of the two quantum states in Hilbert space. The bound is linked to the feasibility of the evolutions of the state vectors, and provides a tighter upper bound. In addition, the generalized Margolus-Levitin bound is discussed.
We report on a time-scaling technique to enhance the performances of quantum control protocols in non-Hermitian systems. The considered time scaling involves no extra couplings and yields a significant enhancement of the quantum fidelity for a comparable amount of resources. We discuss the application of this technique to quantum-state transfers in two- and three-level open quantum systems. We derive the quantum speed limit in a system governed by a non-Hermitian Hamiltonian. Interestingly, we show that with an appropriate driving the time-scaling technique preserves the optimality of the quantum speed with respect to the quantum speed limit whereas reducing significantly the damping of the quantum-state norm.
We discuss a class of quantum speed limits (QSLs) based on unified quantum ($\ensuremath{\alpha},\ensuremath{\mu}$)-entropy for nonunitary physical processes. The bounds depend on both the Schatten speed and the smallest eigenvalue of the evolved state and the two-parametric unified entropy. We specialize these results to quantum channels and non-Hermitian evolutions. In the first case, the QSL depends on the Kraus operators related to the quantum channel, while in the second case the speed limit is recast in terms of the non-Hermitian Hamiltonian. To illustrate these findings, we consider a single-qubit state evolving under the (i) amplitude damping channel and (ii) the nonunitary dynamics generated by a parity-time-reversal symmetric non-Hermitian Hamiltonian. The QSL is nonzero at earlier times, while it becomes loose as the smallest eigenvalue of the evolved state approaches zero. Furthermore, we investigate the interplay between unified entropies and speed limits for the reduced dynamics of quantum many-body systems. The unified entropy is upper bounded by the quantum fluctuations of the Hamiltonian of the system, while the QSL is nonzero when entanglement is created by the nonunitary evolution. Finally, we apply these results to the XXZ model and verify that the QSL asymptotically decreases as the system size increases. Our results find applications to nonequilibrium thermodynamics, quantum metrology, and equilibration of many-body systems.