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

Kil-Chan Ha, Kyung Hoon Han, 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 is strong enough to get nonzero volume of entanglement with positive partial transposes.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 is strong enough to get nonzero volume of entanglement with positive partial transposes.

arXiv:1803.00175Mar 1, 20180 citations

Criteria excluding full separability of multi-qubit quantum states

Otfried Gühne

Sep 20, 20100 citations

Eigenvalues, separability and absolute separability of two-qubit states

Paul B. Slater

arXiv:0805.0267Journal of Geometry and PhysicsSep 7, 200817 citations

Separability criterion for three-qubit states with a four dimensional norm

Lin Chen, Kyung Hoon Han, Seung-Hyeok Kye

Abstract We give a separability criterion for three qubit states in terms of diagonal and anti-diagonal entries. This gives us a complete characterization of separability when all the entries are zero except for diagonal and anti-diagonals. The criterion is expressed in terms of a norm arising from anti-diagonal entries. We compute this norm in several cases, so that we get criteria with which we can decide the separability by routine computations.

arXiv:1705.05557Journal of Physics A Mathematical and TheoreticalJul 13, 20178 citations

Entanglement criteria and full separability of multi-qubit quantum states

Otfried Gühne

arXiv:1009.3782Physics Letters ANov 14, 201040 citations

The role of phases in detecting three-qubit entanglement

Kyung Hoon Han, Seung-Hyeok Kye

We propose separability criteria for three-qubit states in terms of diagonal and anti-diagonal entries to detect entanglement with positive partial transposes. We report that the phases, that is, the angular parts of anti-diagonal entries, play a crucial role in determining whether a given three-qubit state is separable or entangled, and they must obey even an identity for separability in some cases. These criteria are strong enough to detect PPT (positive partial transpose) entanglement with nonzero volume. In several cases when all the entries are zero except for diagonal and anti-diagonal entries, we characterize separability using phases. These include the cases when anti-diagonal entries of such states share a common magnitude, and when ranks are less than or equal to six. We also compute the lengths of rank six cases and find three-qubit separable states with lengths 8 whose maximum ranks of partial transposes are 7.We propose separability criteria for three-qubit states in terms of diagonal and anti-diagonal entries to detect entanglement with positive partial transposes. We report that the phases, that is, the angular parts of anti-diagonal entries, play a crucial role in determining whether a given three-qubit state is separable or entangled, and they must obey even an identity for separability in some cases. These criteria are strong enough to detect PPT (positive partial transpose) entanglement with nonzero volume. In several cases when all the entries are zero except for diagonal and anti-diagonal entries, we characterize separability using phases. These include the cases when anti-diagonal entries of such states share a common magnitude, and when ranks are less than or equal to six. We also compute the lengths of rank six cases and find three-qubit separable states with lengths 8 whose maximum ranks of partial transposes are 7.

arXiv:1610.06645Journal of Mathematical PhysicsOct 1, 20178 citations

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

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