Detection efficiency and noise in semi-device independent randomness extraction protocol

TL;DR

This paper investigates the detection efficiency thresholds and optimal averaging methods for semi-device independent quantum randomness generation, providing analytical relationships to enhance randomness extraction in practical experiments.

Contribution

It identifies critical detection efficiency thresholds and derives an analytical relationship between guessing probability and dimension witness for improved randomness generation.

Findings

Critical detection efficiency is 0.7071 in symmetric setups.

Asymmetric setups allow near-zero efficiency if one basis is perfect.

Proper averaging methods depend on the dimension witness value.

Abstract

In this paper, we analyze several critical issues in semi-device independent quantum information processing protocol. In practical experimental realization randomness generation in that scenario is possible only if the efficiency of the detectors used is above a certain threshold. Our analysis shows that the critical detection efficiency is 0.7071 in the symmetric setup, while in the asymmetric setup if one of the bases has perfect critical detection efficiency then the other one can be arbitrarily close to 0. We also analyze the semi-device independent random number generation efficiency based on different averages of guessing probability. To generate more randomness, the proper averaging method should be applied. Its choice depends on the value of a certain dimension witness. More importantly, the general analytical relationship between the maximal average guessing probability and dimension witness is given.