Computing the maximum violation of a Bell inequality is NP-complete

TL;DR

Maximizing Bell inequality violations is computationally hard, proven to be NP-complete, implying significant challenges in quantifying quantum nonlocality for systems with many qubits.

Contribution

This paper proves that optimizing Bell inequality violations is an NP-complete problem, establishing its computational intractability for arbitrary quantum systems.

Findings

Optimization steps grow exponentially with system size

Bell inequality maximization is NP-complete

Implications for quantifying quantum nonlocality

Abstract

The number of steps required in order to maximize a Bell inequality for arbitrary number of qubits is shown to grow exponentially with either the number of steps and the number of parties involved. The proof that the optimization of such correlation measure is a NP-problem is based on an operational perspective involving a Turing machine, which follows a general algorithm. The implications for the computability of the so called {\it nonlocality} for any number of qubits is similar to recent results involving entanglement or similar quantum correlation-based measures.