We interpret multi-partite genuine entanglement witnesses as simultaneous positivity of various maps arising from them. apply this result to multi-qubit {\sf X}-shaped Hermitian matrices, and characterize the conditions for them be witnesses, in terms entries. Furthermore, we find all optimal ones among They turn out have spanning properties, so they detect non-zero volume set entanglement. also decomposability witnesses.

We consider bi-linear analogues of s-positivity for linear maps. The dual objects these notions can be described in terms Schmidt ranks tri-tensor products and numbers tri-partite quantum states. These versions cover various kinds bi-separability, so we may interpret witnesses those give concrete examples three qubit entanglement.

We characterize the separability of three qubit GHZ diagonal states in terms entries. This enables us to check without decomposition into sum pure product states. In course discussion, we show that necessary criterion Gühne (2011 Entanglement criteria and full multi-qubit quantum Phys. Lett. A 375 406–10) for (full) is sufficient with a simpler formula. The main tool use entanglement witnesses which are tri-partite Choi matrices positive bi-linear maps.

We construct seven kinds of three-qubit biseparable states to show that every class in the partial separability classification proposed by Szalay and K\"ok\'enyesi [S. Z. K\"ok\'enyesi, Phys. Rev. A 86, 032341 (2012)] is nonempty.

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

In order to classify partial entanglement of multi-partite states, it is natural consider the convex hulls, intersections and differences basic cones obtained from partially separable states with respect partitions systems. this paper, we consisting X-shaped three qubit arising in way. The class includes important classes like Greenberger-Horne-Zeilinger diagonal states. We find all extreme rays those exhibit corresponding also give characterizations for which rise necessary criteria terms...

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

In this paper, we consider all possible variants of Choi matrices linear maps, and show that they are determined by non-degenerate bilinear forms on the domain space. We will do in setting finite dimensional vector spaces. case matrix algebras, characterize which retain usual correspondences between k-superpositivity Schmidt number ≤k as well k-positivity k-block-positivity. also compare de Pillis’ definition [Pac. J. Math. 23, 129–137 (1967)] Choi’s [Linear Algebra Appl. 10, 285–290...

We show that noncommutative <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L Subscript p"> <mml:semantics> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">L_p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-spaces satisfy the axioms of (nonunital) operator system with a dominating constant alttext="2 Superscript StartFraction 1 Over p EndFraction">...

Catamenial hemoptysis is a rare condition caused by thoracic endometriosis that presents as tracheobronchial or pulmonary endometriosis. While hormonal treatment may cause virilization and sterility, due to the antiestrogenic effect, its surgical removal via thoracotomy particularly invasive procedure not recommended first choice in young woman. Successful video-assisted thoracoscopic surgery (VATS) has recently been reported, be indicated for patients who at some stage would like become...

In tri-partite systems, there are three basic biseparability, A-BC, B-CA, and C-AB, according to bipartitions of local systems. We begin with convex sets consisting these biseparable states in the three-qubit system, consider arbitrary iterations intersections and/or hulls them get cones. One natural way classify is those which they belong or do not belong. This especially useful partial entanglement mixed states. show that lattice generated by respect hull intersection has infinitely many...

We construct operator systems $\mathfrak C_I$ that are universal in the sense all can be realized as their quotients. They satisfy system lifting property. Without relying on theorem by Kirchberg, we prove Kirchberg type tensor $$\mathfrak C_I \otimes_{\min} B(H) = \mathfrak \otimes_{\max} B(H).$$ Combining this with a result of Kavruk, give new theoretic proof Kirchberg's and show conjecture is equivalent to its analogue =\mathfrak \otimes_{\rm c} C_I.$$ It natural ask whether projective...