Partial separability/entanglement violates distributive rules

• DOI: 10.1007/s11128-020-02710-9
• Publication Date: 2020-06-06T02:02:17Z
• Authors: Kyung Hoon Han; Seung-Hyeok Kye; Szilárd Szalay
• Keywords: Quantum Physics; QC Physics / fizika; 0103 physical sciences; FOS: Physical sciences; Quantum Physics (quant-ph); 01 natural sciences

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.<br/>15 pages, to appear in Quantum Information Processing<br/>