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Partial separability/entanglement violates distributive rules


We found three qubit Greenberger–Horne–Zeilinger diagonal states which tell us that the partial separability of three qubit states violates the distributive rules with respect to the two operations of convex sum and intersection. The gaps between the convex sets involving the distributive rules are of nonzero volume.

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Both KHH and SHK were partially supported by the grant NRF-2017R1A2B4006655, Korea. SzSz was supported by the National Research, Development and Innovation Fund of Hungary within the Researcher-initiated Research Program (Project Nr: NKFIH-K120569) and within the Quantum Technology National Excellence Program (Project Nr: 2017-1.2.1-NKP-2017-00001), by the Ministry for Innovation and Technology within the ÚNKP-19-4 New National Excellence Program, and by the Hungarian Academy of Sciences within the János Bolyai Research Scholarship and the “Lendület” Program.

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Correspondence to Kyung Hoon Han.

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Han, K.H., Kye, SH. & Szalay, S. Partial separability/entanglement violates distributive rules. Quantum Inf Process 19, 202 (2020).

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  • Partially separable
  • Partially entangled
  • Lattice
  • Distributive rule

Mathematics Subject Classification

  • 81P15
  • 15A30
  • 46L05
  • 46L07