Analysis of Bell inequality violation in superconducting qubits

TL;DR

This paper investigates the violation of Bell inequalities in superconducting Josephson phase qubits, considering ideal conditions, measurement errors, decoherence, and crosstalk, and proposes a crosstalk-insensitive Bell inequality variant.

Contribution

It provides a detailed analysis of Bell inequality violation conditions in superconducting qubits, including effects of errors and decoherence, and introduces a crosstalk-insensitive inequality.

Findings

Optimal measurement configurations are identified within specific pseudospin planes.

Measurement crosstalk significantly affects Bell inequality violations.

A modified Bell inequality insensitive to crosstalk is proposed.

Abstract

We analyze conditions for violation of the Bell inequality in the Clauser-Horne-Shimony-Holt form, focusing on the Josephson phase qubits. We start the analysis with maximum violation in the ideal case, and then take into account the effects of the local measurement errors and decoherence. A special attention is paid to configurations of the qubit measurement directions in the pseudospin space lying within either horizontal or vertical planes; these configurations are optimal in certain cases. Besides local measurement errors and decoherence, we also discuss the effect of measurement crosstalk, which affects both the classical inequality and the quantum result. In particular, we propose a version of the Bell inequality which is insensitive to the crosstalk.