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Chinese Physics B

Jensen–Shannon divergence coherence and its quantum speed limit

J. D. Song, Chang‐shui Yu

Published Oct 28, 2025• 0 citations
Publisher

Abstract

Abstract The rate at which quantum coherence is generated or degraded significantly impacts quantum information processing. The minimum time for the coherence-changing process can be well evaluated using the quantum speed limit (QSL), which typically requires taking the maximum across different QSL bounds. In this paper, we derive a coherence QSL bound using the quantum Jensen–Shannon divergence as a coherence measure. It is shown that for any state, there is always a representation in which the dephasing dynamics can saturate the QSL bound. We also numerically demonstrate that our QSL bound can be tighter than previous bounds for some applications. Our results make up for the tightness of the coherence QSL.

DOI
10.1088/1674-1056/ae1821

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Abstract The rate at which quantum coherence is generated or degraded significantly impacts quantum information processing. The minimum time for the coherence-changing process can be well evaluated using the quantum speed limit (QSL), which typically requires taking the maximum across different QSL bounds. In this paper, we derive a coherence QSL bound using the quantum Jensen–Shannon divergence as a coherence measure. It is shown that for any state, there is always a representation in which the dephasing dynamics can saturate the QSL bound. We also numerically demonstrate that our QSL bound can be tighter than previous bounds for some applications. Our results make up for the tightness of the coherence QSL.
We discuss quantum speed limits (QSLs) for finite-dimensional quantum systems undergoing general physical processes. These QSLs were obtained using two families of entropic measures, namely the square root of the Jensen-Shannon divergence, which in turn defines a faithful distance of quantum states, and the square root of the quantum Jeffreys divergence. The results apply to both closed and open quantum systems, and are evaluated in terms of the Schatten speed of the evolved state, as well as cost functions that depend on the smallest and largest eigenvalues of both initial and instantaneous states of the quantum system. To illustrate our findings, we focus on the unitary and nonunitary dynamics of mixed single-qubit states. In the first case, we obtain speed limits aˋ la\textit{à la}aˋ la Mandelstam-Tamm that are inversely proportional to the variance of the Hamiltonian driving the evolution. In the second case, we set the nonunitary dynamics to be described by the noisy operations: depolarizing channel, phase damping channel, and generalized amplitude damping channel. We provide analytical results for the two entropic measures, present numerical simulations to support our results on the speed limits, comment on the tightness of the bounds, and provide a comparison with previous QSLs. Our results may find applications in the study of quantum thermodynamics, entropic uncertainty relations, and also complexity of many-body systems.
Quantum speed limits impose intrinsic lower bounds on the shortest time scale for quantum system evolution. As an emerging paradigm in quantum resource theory, quantum-state texture has attracted research interest amid the rapid advancement of quantum theory. Herein, we investigate the interplay between quantum speed limits and quantum-state texture via several canonical quantifiers, including trace distance, state rugosity and Jensen-Shannon divergence. To demonstrate our findings, we analyze the minimum evolution time of physical systems subject to dephasing and dissipative dynamics. For the Jensen-Shannon divergence, we further explore nonunitary dynamics described by completely positive and trace-preserving maps, taking the amplitude damping channel as a typical example. In addition, we explore the tightness of these bounds in the considered dynamical models. Our results reveal that quantum speed limits derived from quantum-state texture capture the fundamental constraints on quantum evolutionary speed, with promising applications in quantum computing, quantum control and quantum metrology.
Abstract The minimum evolution time between multi-qubit quantum states is estimated for non-Markovian quantum channels. We consider the maximally coherent pure and mixed states as well as multi-qubit X states as initial states and discuss the impact of initial coherence and the behaviour of coherence on their speed of evolution for both dephasing and dissipative processes. The role of the non-zero value of initial coherence under information backflow conditions for the non-unital dissipative process is revealed by the flow of quantum speed limit time ( τ QSL ). The trade-off between mixedness and coherence on the speed limit time reveals the nature of the quantum process the states undergo. The complementarity effect between mixedness and coherence is more prominent in the quantum non-unital dissipation process. The parametric trajectory of speed limit time vividly depicts the difference in the evolution of pure and mixed initial states, and this could be used to distinguish between the unital and non-unital channels studied in this work. Our investigation of quantum speed limit time on multi-qubit entangled X states reveals that τ QSL can be identified as a potential dynamical witness to distinguish multi-qubit states in the course of evolution.
Abstract Recent advances in quantum resource theories have been driven by the fact that many quantum information protocols make use of different facets of the same physical features, e.g. entanglement, coherence, etc. Resource theories formalise the role of these important physical features in a given protocol. One question that remains open until now is: how quickly can a resource be generated or degraded? Using the toolkit of quantum speed limits we construct bounds on the minimum time required for a given resource to change by a fixed increment, which might be thought of as the power of said resource, i.e., the rate of resource variation. We show that the derived bounds are tight by considering several examples. Finally, we discuss some applications of our results, which include generalisations of thermodynamic work, heat, and power to any given resource, as well as fundamental bounds on the computation rate in leading quantum processing architectures.
Quantum speed limits (QSLs) provide an upper bound for the speed of evolution of quantum states in any physical process. Based on the Stratonovich-Weyl correspondence, we derive a universal QSL bound in arbitrary phase spaces that is applicable for both continuous variable systems and finite-dimensional discrete quantum systems. This QSL bound allows the determination of speed limit bounds in specific phase spaces that are tighter than those in Wigner phase space or Hilbert space under the same metric, as illustrated by several typical examples, e.g., a single-mode free field and NNN-level quantum systems in phase spaces. This QSL bound also provides an experimentally realizable way to examine the speed limit in phase spaces relevant to applications in quantum information and quantum optics.
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.