Error-Tolerating Bell Inequalities via Graph States

TL;DR

This paper develops Bell inequalities based on graph states that can tolerate noise and errors, enabling more robust quantum nonlocality tests with practical quantum systems.

Contribution

It introduces a family of error-tolerant Bell inequalities involving graph states that can withstand multiple qubit errors, improving robustness over previous inequalities.

Findings

Constructed Bell inequalities tolerating arbitrary t-qubit errors with 3(t+1) qubits.

Designed a single-error-tolerant Bell inequality with exponentially increasing violation.

Exhaustive search shows the constructions are optimal for up to double errors.

Abstract

We investigate the Bell inequalities derived from the graph states with violations detectable even with the presence of noises, which generalizes the idea of error-correcting Bell inequalities [Phys. Rev. Lett. 101, 080501 (2008)]. Firstly we construct a family of valid Bell inequalities tolerating arbitrary $t$-qubit errors involving $3(t+1)$ qubits, e.g., 6 qubits suffice to tolerate single qubit errors. Secondly we construct also a single-error-tolerating Bell inequality with a violation that increases exponentially with the number of qubits. Exhaustive computer search for optimal error-tolerating Bell inequalities based on graph states on no more than 10 qubits shows that our constructions are optimal for single- and double-error tolerance.