Partial separability/entanglement violates distributive rules

TL;DR

This paper demonstrates that certain three-qubit states exhibit violations of classical distributive rules in quantum entanglement, revealing nonzero volume gaps between convex sets related to partial separability.

Contribution

It identifies specific three-qubit states where partial separability violates distributive rules, highlighting fundamental differences between classical and quantum set relations.

Findings

Partial separability violates distributive rules in three-qubit states.

Gaps between convex sets have nonzero volume.

Identifies specific GHZ diagonal states with these properties.

Abstract

We found three qubit Greenberger-Horne-Zeilinger diagonal states which tells us that the partial separability of three qubit states violates the distributive rules with respect to the two operations of convex sum and intersection. The gaps between the convex sets involving the distributive rules are of nonzero volume.