Quantum Speed limit on the production of quantumness of observables

Abstract

Non-classical features of quantum systems can degrade when subjected to environment and noise. Here, we ask a fundamental question: What is the minimum amount of time it takes for a quantum system to exhibit non-classical features in the presence of noise? Here, we prove distinct speed limits on the quantumness of observable as the norm of the commutator of two given observables. The speed limit on such quantumness measures sets the fundamental upper bound on the rate of change of quantumness, which provides the lower bound on the time required to change the quantumness of a system by a given amount. Additionally, we have proved speed limit for the non-classical features such as quantum coherence that captures the amount of superposition in the quantum systems. We have demonstrated that obtained speed limits are attainable for physical processes of interest, and hence, these bounds can be considered to be tight.