Bell Inequalities Induced by Pseudo Pauli Operators on Single Logical Qubits

TL;DR

This paper introduces a general quantum-to-classical approach using pseudo Pauli operators to construct and understand Bell inequalities, including new variants and their connection to uncertainty relations.

Contribution

It develops a novel framework for deriving Bell inequalities from pseudo Pauli operators, broadening the understanding of Bell nonlocality and uncertainty relations.

Findings

Derived new Bell inequalities using pseudo Pauli operators

Connected quadratic Bell inequalities to uncertainty relations

Provided a unified approach for constructing Bell inequalities

Abstract

In most Bell tests, the measurement settings are specially chosen so that the maximal quantum violations of the Bell inequalities can be detected, or at least, the violations are strong enough to be observed. Such choices can usually associate the corresponding Bell operators to a kind of effective observables, called pseudo Pauli operators, providing us a more intuitive understanding of Bell nonlocality in some sense. Based on that, a more general quantum-to-classical approach for the constructions of Bell inequalities is developed. Using this approach, one can not only derive several kinds of well-known Bell inequalities, but also explore many new ones. Besides, we show that some quadratic Bell inequalities can be induced from the uncertainty relations of pseudo Pauli operators as well, which may shed new light on the study of uncertainty relations of some nonlocal observables.