On operational approach to entanglement and how to certify it

TL;DR

This paper clarifies the operational distinctions between entangled and separable states, emphasizing the challenges in experimentally certifying entanglement due to potential violations of inequalities and issues with statistical testing.

Contribution

It provides a clear operational framework for understanding entanglement and discusses the difficulties in its experimental certification, challenging the notion that all quantum states are entangled.

Findings

Violation of Bell and steering inequalities indicates entanglement.

Experiments outside quantum physics can violate these inequalities.

Certifying entanglement experimentally is challenging due to statistical issues.

Abstract

Entangled physical systems are an important resource in quantum information. Some authors claim that in fact all quantum states are entangled. In this paper we show that this claim is incorrect and we discuss in operational way differences existing between separable and entangled states. A sufficient condition for entanglement is the violation of Bell- CHSH-CH inequalities and/or steering inequalities. Since there exist experiments outside the domain of quantum physics violating these inequalities therefore in the operational approach one cannot say that the entanglement is an exclusive quantum phenomenon. We also explain that an unambiguous experimental certification of the entanglement is a difficult task because classical statistical significance tests may not be trusted if sample homogeneity cannot be tested or is not tested carefully enough.