Journal
QUANTUM INFORMATION PROCESSING
Volume 20, Issue 4, Pages -Publisher
SPRINGER
DOI: 10.1007/s11128-021-03095-z
Keywords
Partial entanglement; separability; Distributive rules; Three-qubit states; X-shaped
Funding
- [NRF-2020R1A2C1A01004587]
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In this note, criteria for three-qubit partially entangled states arising from distributive rules are provided, along with corresponding witnesses. The criteria are given in terms of diagonal and anti-diagonal entries, characterizing partial entanglement completely when all entries are zero except for diagonal and anti-diagonal entries. Important states like Greenberger-Horne-Zeilinger diagonal states fall under this category.
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.
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