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arXiv:2509.20347 · Physical Review A

Quantum speed limits based on Jensen-Shannon and Jeffreys divergences for general physical processes

Jucelino Ferreira de Sousa, Diego Paiva Pires

Published Mar 16, 2026• 1 citation
arXivHTMLPDF

Abstract

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 $\textit{à la}$ 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.

DOI
10.1103/qnd8-dww7

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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.
We present a class of generalized entropic quantum speed limits based on ααα-zzz-Rényi relative entropy, a real-valued, contractive, two-parameter family of distinguishability measures. The quantum speed limit (QSL) falls into the class of Mandelstam-Tamm bounds, and applies to finite-dimensional quantum systems that undergo a general physical process, i.e., their effective dynamics can be modeled by unitary or nonunitary evolutions. The results cover pure or mixed, separable, and entangled probe quantum states. The QSL time depends on the smallest and largest eigenvalues of the probe and instantaneous states of the system, and its evaluation requires low computational cost. In addition, it is inversely proportional to the time-average of the Schatten speed of the instantaneous state, which in turn is fully characterized by the considered dynamics. We specialize our results to the case of unitary and nonunitary evolutions. In the former case, the QSL scales with the inverse of the energy fluctuations, while the latter depends on the Schatten 111-norm of the rate of change of the quantum channel Kraus operators. We illustrate our findings for single-qubit and two-qubit states, and unitary and nonunitary evolutions. Our results may find applications in the study of entropic uncertainty relations, quantum metrology, and also entanglement entropies signaled by generalized entropies.
Quantum speed limits (QSLs) establish intrinsic bounds on the minimum time required for the evolution of quantum systems. We present a class of QSLs formulated in terms of the two-parameter Sharma-Mittal entropy (SME), applicable to finite-dimensional systems evolving under general nonunitary dynamics. In the single-qubit case, the QSLs for both quantum channels and non-Hermitian dynamics are analyzed in detail. For many-body systems, we explore the role of SME-based bounds in characterizing the reduced dynamics and apply the results to the XXZ spin chain model. These entropy-based QSLs characterize fundamental limits on quantum evolution speeds and may be employed in contexts including entropic uncertainty relations, quantum metrology, coherent control and quantum sensing.
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 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.
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.
In this work, we investigate the role of functionals of generalized fidelity measures in deriving quantum speed limits (QSLs) within a geometric approach. We establish a general theoretical framework and show that, once a specific generalized fidelity is selected, the resulting Margolus-Levitin and Mandelstam-Tamm QSLs for both unitary and nonunitary (Lindblad-type) dynamics depend solely on the chosen fidelity measure. We prove that any monotone, differentiable reparametrization of the chosen fidelity yields exactly the same Margolus-Levitin and Mandelstam-Tamm-type QSL, rendering the QSLs invariant under such transformations and thereby unifying fidelity- and metric-induced geometric formulations. This result highlights the limitations of improving QSLs through functional transformations of fidelity and indicates that genuine improvements must arise from alternative fidelity definitions. We further show that several QSLs reported in the literature are encompassed by our framework and discuss possible extensions based on other generalized fidelity measures beyond those explicitly analyzed. In addition, we consider the damped Jaynes-Cummings model as a concrete physical setting to explore the behavior of the QSLs discussed in this work and analyze their regime-dependent features.