Quantum speed limit for Kirkwood-Dirac quasiprobabilities
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This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
Abstract
What is the minimal time until a quantum system can exhibit genuine quantum features? To answer this question we derive quantum speed limits for two-time correlation functions arising from statistics of measurements. Generally, these two-time correlators are described by quasiprobabilities, if the initial quantum state of the system does not commute with the measurement observables. Our quantum speed limits are derived from the Heisenberg-Robertson uncertainty relation, and set the minimal time at which a quasiprobability can become non-positive, which is evidence for the onset of non-classical traits in the system dynamics. As an illustrative example, we apply these results to a conditional quantum gate, by determining the optimal condition giving rise to non-classicality at maximum speed. Our analysis also hints at boosted power extraction in genuinely non-classical dynamics.