16,641 research outputs found

    Decomposability of Linear Maps under Tensor Products

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    Both completely positive and completely copositive maps stay decomposable under tensor powers, i.e under tensoring the linear map with itself. But are there other examples of maps with this property? We show that this is not the case: Any decomposable map, that is neither completely positive nor completely copositive, will lose decomposability eventually after taking enough tensor powers. Moreover, we establish explicit bounds to quantify when this happens. To prove these results we use a symmetrization technique from the theory of entanglement distillation, and analyze when certain symmetric maps become non-decomposable after taking tensor powers. Finally, we apply our results to construct new examples of non-decomposable positive maps, and establish a connection to the PPT squared conjecture.Comment: 26 pages, 3 figure

    A class of 2^N x 2^N bound entangled states revealed by non-decomposable maps

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    We use some general results regarding positive maps to exhibit examples of non-decomposable maps and 2^N x 2^N, N >= 2, bound entangled states, e.g. non distillable bipartite states of N + N qubits.Comment: 19 pages, 1 figur

    On strongly freely decomposable and induced maps

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    Freely decomposable and strongly freely decomposable maps were introduced by G. R. Gordh and C. B. Hughes as a generalization of monotone maps with the property that these maps preserve local connectedness in inverse limits. We prove some relationships between f, Cn(f) and 2f, when f, Cn(f) or 2f belong to the following classes of maps: Almost monotone, quasi-monotone, weakly monotone, freely decomposable or strongly freely decomposable. We correct two corollaries formulated by Jaunusz J. Charatonik in ``On feebly monotone and related classes of maps\u27\u27. We also present an alternative reformulation of these results

    Facial structures for various notions of positivity and applications to the theory of entanglement

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    In this expository note, we explain facial structures for the convex cones consisting of positive linear maps, completely positive linear maps, decomposable positive linear maps between matrix algebras, respectively. These will be applied to study the notions of entangled edge states with positive partial transposes and optimality of entanglement witnesses.Comment: An expository note. Section 7 and Section 8 have been enlarge

    Generalized qudit Choi maps

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    Following the linear programming prescription of Ref. \cite{PRA72}, the d⊗dd\otimes d Bell diagonal entanglement witnesses are provided. By using Jamiolkowski isomorphism, it is shown that the corresponding positive maps are the generalized qudit Choi maps. Also by manipulating particular d⊗dd\otimes d Bell diagonal separable states and constructing corresponding bound entangled states, it is shown that thus obtained d⊗dd\otimes d BDEW's (consequently qudit Choi maps) are non-decomposable in certain range of their parameters.Comment: 22 page
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