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 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. Hence, the speed vanishes in the corresponding classical limit. 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 probability to a target measurement probability and apply this result to analyzing the cost of generating a local athermality in terms of genuine quantum uncertainty.

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• Quantum foundations
• Quantum information processing
• Quantum measurements
• Quantum metrology