Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments

TL;DR

This paper explores the role of mutually unbiased bases and symmetric informationally complete measurements in quantum nonlocality, providing new Bell inequalities, certification methods, and protocols for quantum cryptography.

Contribution

It introduces Bell inequalities maximally violated by MUBs and SICs, and develops device-independent certification and protocols leveraging these structures.

Findings

Bell inequalities maximally violated by MUBs and SICs

Device-independent certification of MUBs and SICs

Protocols for quantum key distribution and random number generation

Abstract

Mutually unbiased bases (MUBs) and symmetric informationally complete projectors (SICs) are crucial to many conceptual and practical aspects of quantum theory. Here, we develop their role in quantum nonlocality by: i) introducing families of Bell inequalities that are maximally violated by $d$-dimensional MUBs and SICs respectively, ii) proving device-independent certification of natural operational notions of MUBs and SICs, and iii) using MUBs and SICs to develop optimal-rate and nearly optimal-rate protocols for device independent quantum key distribution and device-independent quantum random number generation respectively. Moreover, we also present the first example of an extremal point of the quantum set of correlations which admits physically inequivalent quantum realisations. Our results elaborately demonstrate the foundational and practical relevance of the two most important discrete Hilbert space structures to the field of quantum nonlocality.