Quantum speed limit for observables from quantum asymmetry

TL;DR

This paper establishes a quantum speed limit for observables based on quantum asymmetry, linking it to coherence, Fisher information, and thermodynamics, with experimental and theoretical implications.

Contribution

It introduces a novel formulation of quantum speed limits for observables using trace-norm asymmetry, connecting quantum resources to dynamical bounds.

Findings

Derived a trace-norm asymmetry-based quantum speed limit for observables.

Demonstrated the speed limit's relation to quantum Fisher information and coherence.

Applied the framework to quantum thermodynamics, establishing a speed limit in that context.

Abstract

Quantum asymmetry and coherence are genuinely quantum resources that are essential to realize quantum advantage in information technologies. However, all quantum processes are fundamentally constrained by quantum speed limits, which raises the question on the corresponding bounds on the rate of consumption of asymmetry and coherence. In the present work, we derive a formulation of the quantum speed limit for observables in terms of the trace-norm asymmetry of the time-dependent quantum state relative to the observable. This quantum speed limit can be directly observed in experiment through weak value measurement and provides a lower bound to the quantum Fisher information about the parameter conjugate to the observable. It can be further related to quantum coherence relative to the eigenbasis of the observable. We obtain a complementary relation for the speed of three mutually unbiased observables for a single qubit. As an application, we derive a notion of a quantum thermodynamic speed limit.