Criteria for partial entanglement of three qubit states arising from distributive rules

Abstract

It is known that the partial entanglement/separability violates distributive rules with respect to the operations of taking convex hull and intersection. In this note, we give criteria for three qubit partially entangled states arising from distributive rules, together with the corresponding witnesses. The criteria will be given in terms of diagonal and anti-diagonal entries. They actually characterize those partial entanglement completely when all the entries are zero except for diagonal and anti-diagonal entries. Important states like Greenberger-Horne-Zeilinger diagonal states fall down in this class.

24 pages, to appear in Quantum Information Processing

References in corpus (4)

• Partial separability and entanglement criteria for multiqubit quantum states
• Separability criteria for several classes of $n$-partite quantum states
• Partial separability revisited: Necessary and sufficient criteria
• Construction of three-qubit biseparable states distinguishing kinds of entanglement in a partial separability classification