An operational distinction between quantum entanglement and classical non-separability

TL;DR

This paper clarifies the fundamental difference between quantum entanglement and classical non-separability by establishing an operational criterion, resolving ongoing debates about their distinctions despite similar violations of Bell-like inequalities.

Contribution

It introduces a clear operational distinction between quantum entanglement and classical non-separability, addressing a longstanding controversy in the interpretation of Bell inequality violations.

Findings

Quantum entanglement cannot be mimicked by classical non-separable states under the new operational criterion.

Classical non-separability can violate Bell-like inequalities without exhibiting quantum entanglement.

The distinction clarifies the fundamental difference in the nature of correlations in quantum versus classical systems.

Abstract

Quantum entanglement describes superposition states in multi-dimensional systems, at least two partite, which cannot be factorized and are thus non-separable. Non-separable states exist also in classical theories involving vector spaces. In both cases, it is possible to violate a Bell-like inequality. This has led to controversial discussions, which we resolve by identifying an operational distinction between the classical and quantum cases.