Intrinsic randomness under general quantum measurements

TL;DR

This paper investigates the intrinsic randomness generated by general quantum measurements, revealing conditions under which all states produce nonzero randomness and linking randomness to quantum coherence, with implications for quantum random number generation.

Contribution

It introduces a framework for quantifying intrinsic randomness in general measurements and connects it to quantum coherence, extending previous results beyond von Neumann measurements.

Findings

All states have nonzero randomness under symmetric and information-complete measurements.

Intrinsic randomness can be used to design source-independent random number generators.

The work generalizes the resource theory of quantum coherence to include general measurements.

Abstract

Quantum measurements can produce randomness arising from the uncertainty principle. When measuring a state with von Neumann measurements, the intrinsic randomness can be quantified by the quantum coherence of the state on the measurement basis. Unlike projection measurements, there are additional and possibly hidden degrees of freedom in apparatus for generic measurements. We propose an adversary scenario for general measurements with arbitrary input states, based on which, we characterize the intrinsic randomness. Interestingly, we discover that under certain measurements, such as the symmetric and information-complete measurement, all states have nonzero randomness, inspiring a new design of source-independent random number generators without state characterization. Furthermore, our results show that intrinsic randomness can quantify coherence under general measurements, which generalizes the result in the standard resource theory of state coherence.