Certifying randomness in quantum state collapse

TL;DR

This paper establishes a protocol to quantify and verify quantum randomness generated during state collapse, using disturbance effects and allowing for untrusted measurements, with improved efficiency over traditional methods.

Contribution

It introduces a new protocol linking quantum randomness to state collapse, enabling direct estimation and verification with untrusted measurements, enhancing efficiency.

Findings

Higher randomness generation rate than uncertainty-based methods

Effective estimation of randomness via disturbance effects

Protocol accommodates general, untrusted measurements

Abstract

The unpredictable process of state collapse caused by quantum measurements makes the generation of quantum randomness possible. In this paper, we explore the quantitive connection between the randomness generation and the state collapse and provide a randomness verification protocol under the assumptions: (I) independence between the source and the measurement devices and (II) the L\"{u}ders' rule for collapsing state. Without involving heavy mathematical machinery, the amount of genereted quantum randomness can be directly estimated with the disturbance effect originating from the state collapse. In the protocol, we can employ general measurements that are not fully trusted. Equipped with trusted projection measurements, we can further optimize the randomness generation performance. Our protocol also shows a high efficiency and yields a higher randomness generation rate than the one based on uncertainty relation. We expect our results to provide new insights for understanding and generating quantum randomness