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:2607.01035

Susceptibility-kinetic uncertainty relations for quantum systems

Didrik Palmqvist, Ludovico Tesser, Janine Splettstoesser

quant-phcond-mat.mes-hallSubmitted Jul 1, 2026• Announced Jul 2, 2026• 0 citations
arXivHTMLPDF

Abstract

Kinetic uncertainty relations bound current precision of stochastic processes by dynamical activity. The extension of these bounds to quantum systems has been impeded by coherence, strong system-reservoir coupling, and the subtlety of defining dynamical activity in the quantum regime. Here, we introduce a partial dynamical activity through the quantum Fisher information associated with the rescaling of the system-reservoir coupling and show that it bounds current precision via a universal susceptibility-kinetic uncertainty relation. The general validity of this relation for any open quantum system is guaranteed by the natural contribution of a susceptibility term, which is experimentally accessible by tuning the system-reservoir coupling strength. We show how the partial dynamical activity encompasses previous definitions of activity in the weak-coupling Markovian limit and that it provides an information-geometric interpretation of correlator-based activities. We illustrate the tight constraint on precision that our bound provides with the example of steady-state transport through a double quantum dot, where quantum effects invalidate previously developed kinetic uncertainty relations. We expect our bound to provide a powerful tool for optimizing precision in arbitrary quantum systems.

Comments
15 pages, 7 figures

Related papers

Quantum Kinetic Uncertainty Relations in Mesoscopic Conductors at Strong Coupling

Gianmichele Blasi, Ricard Ravell Rodríguez, Michael V. Moskalets +2 more

Kinetic uncertainty relations (KURs) set fundamental limits on the precision of nonequilibrium transport by bounding the signal-to-noise ratio of currents in terms of the dynamical activity, a quantity that counts exchange events between a system and its reservoirs. This framework is well established in the weak-coupling regime, where transport occurs via well-defined, particlelike tunneling processes. At strong coupling, however, quantum coherence challenges both the validity of standard KURs and the notion of activity itself. In this Letter, we introduce a generalized definition of dynamical activity valid at arbitrary system-reservoir coupling, and show that it leads to a breakdown of standard KURs at strong coupling. Building on this result, we derive and prove a novel uncertainty relation, denoted quantum KUR (QKUR), which provides a genuine quantum extension of KUR, accounting for intrinsic quantum coherent contributions of the generalized activity. We demonstrate that the generalized activity reduces to the standard master-equation definition in the weak-coupling regime for generic systems of N coupled quantum dots described by a quadratic Hamiltonian, and analyze the resulting QKUR bound in paradigmatic quantum-coherent mesoscopic devices, including single- and double-quantum dot systems and a quantum point contact.

arXiv:2505.13200•Physical Review Letters•May 19, 2026•1 citation

Fundamental Bounds on Precision and Response for Quantum Trajectory Observables

Tan Van Vu

The precision and response of trajectory observables offer valuable insights into the behavior of nonequilibrium systems. For classical systems, trade-offs between these characteristics and thermodynamic costs, such as entropy production and dynamical activity, have been established through uncertainty relations. Quantum systems, however, present unique challenges, where quantum coherence can enhance precision and violate classical uncertainty relations. In this study, we derive trade-off relations for stochastic observables in Markovian open quantum systems. Specifically, we present three key results: (i) a quantum generalization of the thermokinetic uncertainty relation, which bounds the relative fluctuations of currents in terms of entropy production and dynamical activity; (ii) a quantum inverse uncertainty relation, which constrains the relative fluctuations of arbitrary counting observables based on their instantaneous fluctuations and the spectral gap of the symmetrized Liouvillian; and (iii) a quantum response kinetic uncertainty relation, which bounds the response of general observables to kinetic perturbations in terms of dynamical activity. These fundamental bounds, validated numerically using a three-level maser and a boundary-driven X X Z spin chain, provide a comprehensive framework for understanding the interplay between precision, response, and thermodynamic costs in quantum systems.

arXiv:2411.19546•PRX Quantum•Mar 6, 2025•26 citations

Kinetic Uncertainty Relations for Quantum Transport

Didrik Palmqvist, Ludovico Tesser, Janine Splettstoesser

We analyze the precision of generic currents in a multiterminal quantum-transport setting. Employing scattering theory, we show that the precision of such currents is limited by a function of the particle-current noise that can be interpreted as the activity in the classical limit. We thereby establish a kinetic uncertainty relation for quantum transport. In the full quantum limit, we find precision bounds with modified activity constraints depending on whether the system is fermionic or bosonic. We expect these bounds to be suitable as guidelines for any transport process aiming at high precision.

arXiv:2410.10793•Physical Review Letters•Sep 22, 2025•11 citations

Universal Precision Limits in General Open Quantum Systems

Tan Van Vu, Ryotaro Honma, Keiji Saito

The intuition that the precision of observables is constrained by thermodynamic costs has recently been formalized through thermodynamic and kinetic uncertainty relations. While such trade-offs have been extensively studied in Markovian systems, corresponding constraints in the non-Markovian regime remain largely unexplored. In this Letter, we derive universal bounds on the precision of generic observables in open quantum systems that interact with their environments at arbitrary coupling strengths and are subjected to two-point measurements. By introducing an asymmetry term that quantifies the disparity between forward and backward processes, we show that the relative fluctuation of any time-antisymmetric current is constrained not only by entropy production but also by this asymmetry. For general observables, we further prove that their relative fluctuation is always bounded from below by a generalized activity term that characterizes environmental changes. These results establish a comprehensive framework for understanding the fundamental limits of precision in a broad class of open quantum systems, beyond the traditional Markovian setting.

arXiv:2508.21567•Physical Review Letters•Mar 26, 2026•1 citation

Characterizing quantum precision enhancement for multiple currents in open quantum systems

Khalak Mahadeviya, Sheikh Parvez Mandal, Mahasweta Pandit +3 more

The kinetic uncertainty relation (KUR) constrains fluctuations of individual currents in classical nonequilibrium systems in terms of the dynamical activity, which quantifies the average number of transitions per unit of time. Here, we derive a multi-current KUR (MKUR) establishing the precision limit for multiple currents generated in classical stochastic processes in the nonequilibrium steady state. We then apply our theory to identify quantum devices whose correlated current fluctuations surpass this classical limit by comparing the quantum system to a classical emulator with the same average currents in the steady state. In this way, violations of the emulator's MKUR have a clear physical meaning, i.e., that the quantum-coherent evolution reduces joint current fluctuations below what is possible for a classical Markovian system with the same energy-level structure and incoherent resources. Since the MKUR incorporates correlations between currents, its violation pinpoints nonclassical fluctuations in parameter regimes where the single-current KUR is satisfied. We illustrate the essential and complementary role of these bounds for characterizing joint current precision with two examples: a coherently driven two-level system and an experimentally motivated model of a three-level heat engine subject to parasitic environmental couplings.

quant-pharXiv:2609.35982•Sep 30, 2026•0 citations

Response kinetic uncertainty relation for Markovian open quantum systems

Kangqiao Liu, Jie Gu

Response uncertainty relations in stochastic thermodynamics extend precision bounds to the sensitivity of observables under external perturbations. Here we derive a quantum response kinetic uncertainty relation for continuously monitored Markovian open quantum systems in the steady state of the Lindblad master equation. The response precision of a measured trajectory observable is bounded by two contributions: the conventional quantum dynamical activity and a perturbation-induced intersubspace transition term. The latter is absent in the classical limit and captures a genuinely quantum part of the response cost. We identify simple conditions under which either contribution vanishes, and we further clarify the structure of the intersubspace term through a symmetry-resolved decomposition and exact sector-selection rules. The bound and its structure are illustrated in a driven two-level atom.

arXiv:2501.04895•Physical Review A•Jun 16, 2026•1 citation
Kinetic uncertainty relations bound current precision of stochastic processes by dynamical activity. The extension of these bounds to quantum systems has been impeded by coherence, strong system-reservoir coupling, and the subtlety of defining dynamical activity in the quantum regime. Here, we introduce a partial dynamical activity through the quantum Fisher information associated with the rescaling of the system-reservoir coupling and show that it bounds current precision via a universal susceptibility-kinetic uncertainty relation. The general validity of this relation for any open quantum system is guaranteed by the natural contribution of a susceptibility term, which is experimentally accessible by tuning the system-reservoir coupling strength. We show how the partial dynamical activity encompasses previous definitions of activity in the weak-coupling Markovian limit and that it provides an information-geometric interpretation of correlator-based activities. We illustrate the tight constraint on precision that our bound provides with the example of steady-state transport through a double quantum dot, where quantum effects invalidate previously developed kinetic uncertainty relations. We expect our bound to provide a powerful tool for optimizing precision in arbitrary quantum systems.
Kinetic uncertainty relations (KURs) set fundamental limits on the precision of nonequilibrium transport by bounding the signal-to-noise ratio of currents in terms of the dynamical activity, a quantity that counts exchange events between a system and its reservoirs. This framework is well established in the weak-coupling regime, where transport occurs via well-defined, particlelike tunneling processes. At strong coupling, however, quantum coherence challenges both the validity of standard KURs and the notion of activity itself. In this Letter, we introduce a generalized definition of dynamical activity valid at arbitrary system-reservoir coupling, and show that it leads to a breakdown of standard KURs at strong coupling. Building on this result, we derive and prove a novel uncertainty relation, denoted quantum KUR (QKUR), which provides a genuine quantum extension of KUR, accounting for intrinsic quantum coherent contributions of the generalized activity. We demonstrate that the generalized activity reduces to the standard master-equation definition in the weak-coupling regime for generic systems of N coupled quantum dots described by a quadratic Hamiltonian, and analyze the resulting QKUR bound in paradigmatic quantum-coherent mesoscopic devices, including single- and double-quantum dot systems and a quantum point contact.
The precision and response of trajectory observables offer valuable insights into the behavior of nonequilibrium systems. For classical systems, trade-offs between these characteristics and thermodynamic costs, such as entropy production and dynamical activity, have been established through uncertainty relations. Quantum systems, however, present unique challenges, where quantum coherence can enhance precision and violate classical uncertainty relations. In this study, we derive trade-off relations for stochastic observables in Markovian open quantum systems. Specifically, we present three key results: (i) a quantum generalization of the thermokinetic uncertainty relation, which bounds the relative fluctuations of currents in terms of entropy production and dynamical activity; (ii) a quantum inverse uncertainty relation, which constrains the relative fluctuations of arbitrary counting observables based on their instantaneous fluctuations and the spectral gap of the symmetrized Liouvillian; and (iii) a quantum response kinetic uncertainty relation, which bounds the response of general observables to kinetic perturbations in terms of dynamical activity. These fundamental bounds, validated numerically using a three-level maser and a boundary-driven X X Z spin chain, provide a comprehensive framework for understanding the interplay between precision, response, and thermodynamic costs in quantum systems.
We analyze the precision of generic currents in a multiterminal quantum-transport setting. Employing scattering theory, we show that the precision of such currents is limited by a function of the particle-current noise that can be interpreted as the activity in the classical limit. We thereby establish a kinetic uncertainty relation for quantum transport. In the full quantum limit, we find precision bounds with modified activity constraints depending on whether the system is fermionic or bosonic. We expect these bounds to be suitable as guidelines for any transport process aiming at high precision.
The intuition that the precision of observables is constrained by thermodynamic costs has recently been formalized through thermodynamic and kinetic uncertainty relations. While such trade-offs have been extensively studied in Markovian systems, corresponding constraints in the non-Markovian regime remain largely unexplored. In this Letter, we derive universal bounds on the precision of generic observables in open quantum systems that interact with their environments at arbitrary coupling strengths and are subjected to two-point measurements. By introducing an asymmetry term that quantifies the disparity between forward and backward processes, we show that the relative fluctuation of any time-antisymmetric current is constrained not only by entropy production but also by this asymmetry. For general observables, we further prove that their relative fluctuation is always bounded from below by a generalized activity term that characterizes environmental changes. These results establish a comprehensive framework for understanding the fundamental limits of precision in a broad class of open quantum systems, beyond the traditional Markovian setting.
The kinetic uncertainty relation (KUR) constrains fluctuations of individual currents in classical nonequilibrium systems in terms of the dynamical activity, which quantifies the average number of transitions per unit of time. Here, we derive a multi-current KUR (MKUR) establishing the precision limit for multiple currents generated in classical stochastic processes in the nonequilibrium steady state. We then apply our theory to identify quantum devices whose correlated current fluctuations surpass this classical limit by comparing the quantum system to a classical emulator with the same average currents in the steady state. In this way, violations of the emulator's MKUR have a clear physical meaning, i.e., that the quantum-coherent evolution reduces joint current fluctuations below what is possible for a classical Markovian system with the same energy-level structure and incoherent resources. Since the MKUR incorporates correlations between currents, its violation pinpoints nonclassical fluctuations in parameter regimes where the single-current KUR is satisfied. We illustrate the essential and complementary role of these bounds for characterizing joint current precision with two examples: a coherently driven two-level system and an experimentally motivated model of a three-level heat engine subject to parasitic environmental couplings.
Response uncertainty relations in stochastic thermodynamics extend precision bounds to the sensitivity of observables under external perturbations. Here we derive a quantum response kinetic uncertainty relation for continuously monitored Markovian open quantum systems in the steady state of the Lindblad master equation. The response precision of a measured trajectory observable is bounded by two contributions: the conventional quantum dynamical activity and a perturbation-induced intersubspace transition term. The latter is absent in the classical limit and captures a genuinely quantum part of the response cost. We identify simple conditions under which either contribution vanishes, and we further clarify the structure of the intersubspace term through a symmetry-resolved decomposition and exact sector-selection rules. The bound and its structure are illustrated in a driven two-level atom.