Quantum speed limit for measurement probabilities

TL;DR

This paper establishes a quantum speed limit for transforming measurement probabilities, linking the process to quantum fluctuations and correlations, with implications for quantum information processing efficiency.

Contribution

It introduces a quantum speed limit for measurement probability transformations and demonstrates its role as a witness for quantum correlations.

Findings

Measurement speed constrained by quantum fluctuations

Quantum speed limit can witness bipartite correlations

Minimum transformation time relates to quantum uncertainty in thermality

Abstract

Any protocol to process quantum information has to conclude with a measurement, aimed at producing a specific set of probabilities of measurement outcomes. In this work, we investigate the time, energy and importantly the genuine quantum resources necessary for transforming a set of measurement probabilities generated by a positive-operator-valued measure (POVM), to a target set of measurement probabilities. To this end, we first show that the speed of measurement probabilities, defined as the average rate of the surprisal of measurement outcomes, is constrained by the genuine quantum fluctuations contained in the measurement probabilities. Interestingly, this quantum speed limit can act as a witness for bipartite quantum correlations by selecting an optimal local projective measurement. Furthermore, we obtain a minimum time to transform an initial measurement probabilities to a target measurement probabilities, and apply this result to analyzing the cost of generating a local athermality in terms of genuine quantum uncertainty.