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.
Highlights
What distinguishes the classical world from the underlying quantum domain? Arguably the most prominent answers to this question revolve around the existence of uncertainty relations
We focus on quantum Brownian motion (QBM), which describes the dynamics of a single harmonic oscillator interacting with a bosonic bath [48,49]
That TB is a property of the generator of the nonunitary evolution, and throughout this work we have focused on vanishing quantum speed limit (QSL) times for bounded generators
Summary
What distinguishes the classical world from the underlying quantum domain? Arguably the most prominent answers to this question revolve around the existence of uncertainty relations. In contrast to previous work [27,33], here we do not work with a phase-space representation, but rather develop a QSL theory for Gaussian dynamics directly, which permits us to derive an expression for the QSL time in terms of finite-dimensional matrices using symplectic operators Using this formalism, we discuss three limits in which the QSL time vanishes: (i) → 0, where is interpreted as a parameter of the state, (ii) r → ∞, where r denotes the squeezing in the state, and (iii) n → ∞, where n is the number of modes. By applying our Gaussian QSL theory to general quantum evolution, we discuss the role of classical noise, mixed states, and nonunitary evolution We illustrate how these aspects, which are related to a transition to classical behavior due to incoherent mixing of states rather than reduced uncertainty of observables, cannot decrease the QSL time
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