Qcrypt 2022: Poster132
Violating Bell inequalities with random mutually unbiased bases
Authors
Gelo Noel Tabia (Department of Physics and Center for Quantum Frontiers of Research & Technology (QFort), National Cheng Kung University); Varun Satya Raj Bavana (Department of Physics, Indian Institute of Technology Kharagpur); Shih-Xian Yang (Hon Hai Quantum Computing Research Center); Yeong-Cherng Lia (Department of Physics and Center for Quantum Frontiers of Research & Technology (QFort), National Cheng Kung University)
Abstract
More than just an empirical test of local causality, the demonstration of Bell inequality violations, which can be inferred purely from the observed data, provide a useful tool in various device-independent applications such as random number generation, shared key expansion, and verification of quantum devices. To achieve Bell-nonlocal correlations experimentally often requires the parties involved in the Bell test to have properly calibrated apparatuses and a shared reference frame for their measurements. Therefore it is beneficial to have some relaxation to these nontrivial requirements. To this end, earlier works have shown that for two parties that share a Bell pair, a good chance of violation (41%) is possible if each party selects a random pair of mutually unbiased bases (MUBs). This can be boosted to give almost certain Bell violations if each party measures a uniformly random set of three MUBs.
In this work we examine the probability of generating Bell-inequality-violating correlations by performing randomly chosen MUBs on maximally entangled pair of qudits (d 2). We find that even if we restrict to testing only two-setting Bell inequalities, we find a significant change of Bell violation if the two parties are each allowed to measure a sufficient number of MUBs. In particular, for the case of maximally entangled qutrits and ququarts, our numerical estimates indicate that we can achieve near-guaranteed Bell violation by considering only the two-setting Bell inequalities. For a pair of ququints, the probability remains high but decreases to about 99.84%. Our results suggest that the experimental tests of Bell nonlocality for these higher-dimensional entangled pairs remain viable even when the two parties do not share a common reference frame. More details can be found in arXiv:2205.04037.
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