Kinetic Uncertainty Relation in Collective Dissipative Quantum Many-Body Systems

TL;DR

This paper derives a kinetic uncertainty relation for collective dissipative quantum many-body systems, revealing how interactions can enhance precision scaling with particle number, and provides foundational bounds for quantum technology design.

Contribution

It introduces the first analytical kinetic uncertainty relation for many-body dissipative quantum systems, expanding understanding beyond single-body cases.

Findings

Collective interactions enable precision to scale with particle number.

Derived lower bounds for fluctuations using mean-field approximation.

Validated bounds across different phases of boundary time crystals.

Abstract

Attaining the ultimate precision remains a central objective in the engineering of nanoscale systems and the investigation of nonequilibrium processes. While thermodynamic and kinetic uncertainty relations establish fundamental precision bounds, prior derivations in the quantum regime have remained confined to single-body systems. Consequently, the ultimate precision limits for interacting many-body systems have been unknown. In this Letter, we analytically formulate a kinetic uncertainty relation for a many-body system undergoing collective dissipation, a paradigmatic model of boundary time crystals. By applying a mean-field approximation, we derive lower bounds for relative fluctuations expressed in terms of clear physical quantities. Our analysis identifies a cooperative enhancement mechanism, demonstrating that collective interactions allow the precision to scale with the number of particles. We validate these findings through numerical simulations across the stationary, critical, and boundary time crystal phases. Our work presents the first theoretical description of precision bounds in collective dissipative quantum many-body systems for an arbitrary particle number $N$, providing a solid foundation for designing future quantum technologies that exploit many-body phenomena.