Diverging quantum speed limits: a herald of classicality

TL;DR

This paper investigates when quantum speed limits indicate true quantum behavior versus classicality, revealing that vanishing QSL times often relate to classical features like reduced uncertainty, especially in Gaussian systems.

Contribution

It develops a QSL formalism for Gaussian systems and links classicality indicators to diverging quantum speeds, clarifying the quantum-classical boundary.

Findings

Vanishing QSL times relate to reduced uncertainty in observables.

Large squeezing, small Planck's constant, and large particle number are connected to diverging speeds.

Classical noise increases QSL times, indicating more classical behavior.

Abstract

When is the quantum speed limit (QSL) really quantum? While vanishing QSL times often indicate emergent classical behavior, it is still not entirely understood what precise aspects of classicality are at the origin of this dynamical feature. Here, we show that vanishing QSL times (or, equivalently, diverging quantum speeds) can be traced back to reduced uncertainty in quantum observables and thus can be understood as a consequence of emerging classicality for these particular observables. We illustrate this mechanism by developing a QSL formalism for continuous variable quantum systems undergoing general Gaussian dynamics. For these systems, we show that three typical scenarios leading to vanishing QSL times, namely large squeezing, small effective Planck's constant, and large particle number, can be fundamentally connected to each other. In contrast, by studying the dynamics of open quantum systems and mixed states, we show that the classicality that emerges due to incoherent mixing of states from the addition of classical noise typically increases the QSL time.