Useful multipartite correlations from useless reduced states

TL;DR

This paper demonstrates that certain non-entangled two-qubit states can imply the presence of entanglement in larger systems, revealing that local separable states can still indicate global entanglement.

Contribution

It introduces specific examples of non-entangled states whose compatible larger states must be entangled, highlighting a novel way to infer global entanglement from local data.

Findings

Non-entangled two-qubit states can imply global entanglement.

Local separable states can be compatible only with globally entangled states.

Certain local correlations indicate the presence of genuine tripartite non-local correlations.

Abstract

Understanding what can be inferred about a multi-particle quantum system from only the knowledge of its subparts is a highly non-trivial task. Clearly, if the global system doesn't contain any information resource, nor do its subparts. However, is the converse also true? We show that the answer to is negative. We provide three two-qubit states that are non-entangled, but such that any three-qubit state compatible with them is entangled. Entanglement can thus be deduced from the mere observation of separable reduced states. We extend this finding to correlations and provide local marginal correlations that are only compatible with global genuinely tripartite non-local correlations.