Randomness quantification of coherent detection

TL;DR

This paper develops a quantum-based method to quantify randomness in coherent detection systems, accounting for shot noise and finite local oscillator power, enhancing security analysis in quantum cryptography.

Contribution

It introduces a new measure of randomness for infinite-dimensional quantum systems, extending previous semi-quantum analyses to a full quantum scenario.

Findings

Applicable to general coherent detection systems with finite local oscillator power

Analyzed the randomness generation limits of a vacuum-fluctuation quantum random number generator

Provided a framework for randomness quantification considering shot noise in quantum detection

Abstract

Continuous-variable quantum cryptographic systems, including random number generation and key distribution, are often based on coherent detection. The essence of the security analysis lies in the randomness quantification. Previous analyses employ a semi-quantum picture, where the strong local oscillator limit is assumed. Here, we investigate the randomness of homodyne detection in a full quantum scenario by accounting for the shot noise in the local oscillator, which requires us to develop randomness measures in the infinite-dimensional scenario. Similar to the finite-dimensional case, our introduced measure of randomness corresponds to the relative entropy of coherence defined for an infinite-dimensional system. Our results are applicable to general coherent detection systems, in which the local oscillator is inevitably of finite power. As an application example, we employ the analysis method to a practical vacuum-fluctuation quantum random number generator and explore the limits of generation rate given a continuous-wave laser.