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

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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.

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Authors and Affiliations

  1. Department of Data Science, The University of Suwon, Hwaseong-si, Gyeonggi-do, 445-743, Korea

    Kyung Hoon Han

  2. Department of Mathematics and Institute of Mathematics, Seoul National University, Seoul, 151-742, Korea

    Seung-Hyeok Kye

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  1. Kyung Hoon Han
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  2. Seung-Hyeok Kye
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Correspondence to Kyung Hoon Han.

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Both KHH and SHK were partially supported by NRF-2020R1A2C1A01004587, Korea.

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Han, K.H., Kye, SH. Criteria for partial entanglement of three qubit states arising from distributive rules. Quantum Inf Process 20, 151 (2021). https://doi.org/10.1007/s11128-021-03095-z

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