Hidden Bell correlations in the four-level atom

TL;DR

This paper generalizes Bell inequalities to four-level atomic systems, including superconducting circuits and qudits, providing a broader framework for testing quantum entanglement in higher-dimensional systems.

Contribution

It introduces an extended Bell inequality applicable to four-level atoms and qudits, expanding the scope of entanglement tests beyond two-qubit systems.

Findings

Extended Bell inequality valid for 4x4 Hermitian matrices

Applicable to superconducting circuits and qudits with j=3/2

Framework for distinguishing separable and entangled states

Abstract

We extend the Bell inequality known for two qubits to the four-level atom, including an artificial atom realized by the superconducting circuit, and qudit with j=3/2. We formulate the extended inequality as the inequality valid for an arbitrary Hermitian nonnegative 4x4-matrix with unit trace for both separable and entangled matrices.