Entanglement, detection, and geometry of non-classical States

TL;DR

This paper explores the relationship between non-classical states and entanglement, providing a framework to characterize and detect non-classicality that directly corresponds to entanglement in quantum systems.

Contribution

It introduces a general structure linking non-classicality and entanglement and proposes a scheme for detecting non-classical states with a focus on their geometric properties.

Findings

Established a structure connecting non-classicality and entanglement.

Developed a scheme to detect non-classical states.

Characterized non-classicality that exactly matches entanglement.

Abstract

Non-classical states that are characterized by their non-positive quasi-probabilities in phase space are known to be the basis for various quantum effects. In this work, we investigate the interrelation between the non-classicality and entanglement, and then characterize the non-classicality that precisely corresponds to entanglement. The results naturally follow from two findings: one is the general structure among non-classical, entangled, separable, and classical states over Hermitian operators, and the other a general scheme to detect non-classical states.