Separability of multi-qubit states in terms of diagonal and anti-diagonal entries

  • Kil-Chan Ha
  • Kyung Hoon HanEmail author
  • Seung-Hyeok Kye


We give separability criteria for general multi-qubit states in terms of diagonal and anti-diagonal entries. We define two numbers which are obtained from diagonal and anti-diagonal entries, respectively, and compare them to get criteria. They give rise to characterizations of separability when all the entries are zero except for diagonal and anti-diagonal, like Greenberger–Horne–Zeilinger diagonal states. The criteria are strong enough to detect nonzero volume of entanglement with positive partial transposes.


Multi-qubit states X-states Separability criterion Irreducible balanced multisets Phase identities Phase difference 

Mathematics Subject Classification

81P15 15A30 


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Copyright information

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Authors and Affiliations

  1. 1.Faculty of Mathematics and StatisticsSejong UniversitySeoulKorea
  2. 2.Department of Data ScienceThe University of SuwonHwaseongKorea
  3. 3.Department of Mathematics, Institute of MathematicsSeoul National UniversitySeoulKorea

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