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

Abstract

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.

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Correspondence to Kyung Hoon Han.

Additional information

Both K.H.H. and S.H.K. were partially supported by NRF-2017R1A2B4006655, Korea. K.C.H. was partially supported by NRF-2016R1D1A1A09916730, Korea.

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Ha, K., Han, K.H. & Kye, S. Separability of multi-qubit states in terms of diagonal and anti-diagonal entries. Quantum Inf Process 18, 34 (2019). https://doi.org/10.1007/s11128-018-2145-x

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Keywords

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

Mathematics Subject Classification

  • 81P15
  • 15A30