Quantum speed limit for Kirkwood–Dirac quasiprobabilities

Abstract

What is the minimal time until a quantum system undergoing unitary dynamics can exhibit genuine quantum features? To answer this question we derive quantum speed limits (QSLs) for two-time correlation functions arising from statistics of measurements. These two-time correlators are described by Kirkwood–Dirac quasiprobabilities, if the initial quantum state of the system does not commute with the measurement observables. The QSLs here introduced are derived from the Schrödinger–Robertson uncertainty relation, and set the minimal time at which the real part of a quasiprobability can become negative and the corresponding imaginary part can be different from zero or crosses a given threshold. This departure of Kirkwood–Dirac quasiprobabilities from positivity is evidence for the onset of non-classical traits in the quantum dynamics. As an illustrative example, we apply these results to a conditional quantum gate by determining the optimal condition that gives rise to non-classicality at maximum speed. In this way, our analysis hints at boosted power extraction due to genuinely non-classical dynamics.