Maximal intrinsic randomness of noisy quantum measurements

TL;DR

This paper investigates the maximum amount of private randomness that can be generated from noisy quantum measurements, providing exact solutions for qubit and higher-dimensional cases, and analyzing how noise affects eavesdropper guessing power.

Contribution

It offers a complete solution for the guessing probability of two-outcome qubit measurements and noisy projective measurements in arbitrary dimensions, and compares different noise scenarios.

Findings

Exact guessing probability for two-outcome qubit measurements.

Optimal realizations of measurement distributions with different noise configurations.

Noiseless state with noisy measurement yields higher eavesdropper guessing power.

Abstract

Quantum physics exhibits an intrinsic and private form of randomness with no classical counterpart. Any setup for quantum randomness generation involves measurements acting on quantum states. In this work, we consider the following question: Given a quantum measurement, how much randomness can be generated from it? In real life, measurements are noisy and thus contain an additional, extrinsic form of randomness due to ignorance. This extrinsic randomness is not private since, in an adversarial model, it takes the form of quantum side information held by an eavesdropper who can use it to predict the measurement outcomes. Randomness of measurements is then quantified by the guessing probability of this eavesdropper, when minimized over all possible input states. This optimization is in general hard to compute, but we solve it here for any two-outcome qubit measurement and for projective measurements in arbitrary dimension mixed with white noise. We also construct, for a given measured probability distribution, different realizations with (i) a noisy state and noiseless measurement (ii) a noiseless state and noisy measurement and (iii) a noisy state and measurement, and we show that the latter gives an eavesdropper significantly higher guessing power.