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The structural physical approximation conjecture

Autor: Fred Shultz

Publikováno v: Journal of Mathematical Physics. 57:015218

It was conjectured that the structural physical approximation (SPA) of an optimal entanglement witness is separable (or equivalently, that the SPA of an optimal positive map is entanglement breaking). This conjecture was disproved, first for indecomp

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::281ab9e2cfe1159afac50203b96f7869
https://doi.org/10.1063/1.4938226

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Finding decompositions of a class of separable states

Autor: Fred Shultz, Erik M. Alfsen

By definition a separable state has the form \sum A_i \otimes B_i, where 0 \leq A_i, B_i for each i. In this paper we consider the class of states which admit such a decomposition with B_1, ..., B_p having independent images. We give a simple intrins

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::14466044391c58a2a7d2b44ca2c14195
http://arxiv.org/abs/1202.3673

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Complete positivity of the map from a basis to its dual basis

Autor: Vern I. Paulsen, Fred Shultz

The dual of a matrix ordered space has a natural matrix ordering that makes the dual space matrix ordered as well. The purpose of these notes is to give a condition that describes when the linear map taking a basis of the n by n matrices to its dual

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::17e64029ed0f1e7cc7288d46503e318f

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Unique decompositions, faces, and automorphisms of separable states

Autor: Fred Shultz, Erik M. Alfsen

Let S_k be the set of separable states on B(C^m \otimes C^n) admitting a representation as a convex combination of k pure product states, or fewer. If m>1, n> 1, and k \le max(m,n), we show that S_k admits a subset V_k such that V_k is dense and open

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d8c177c6225c5bbed1a1445d7cf8d5de
http://arxiv.org/abs/0906.1761

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C*-algebras associated with interval maps

Autor: Valentin Deaconu, Fred Shultz

For each piecewise monotonic map tau of [0,1], we associate a pair of C*-algebras F_tau and O_tau and calculate their K-groups. The algebra F_tau is an AI-algebra. We characterize when F_tau and O_\tau are simple. In those cases, F_tau has a unique t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dc0a11d5c5971e6a65ed84409a0c50f1
http://arxiv.org/abs/math/0405469

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Dimension groups for interval maps II: the transitive case

Autor: Fred Shultz

Publikováno v: Ergodic Theory and Dynamical Systems. 27:1287

Any continuous, transitive, piecewise monotonic map is determined up to a binary choice by its dimension module with the associated finite sequence of generators. The dimension module by itself determines the topological entropy of any transitive pie

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::901e32c8757f410f58b3f35f2a13dd10
https://doi.org/10.1017/s014338570700003x

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Akademický článek

C*-algebras associated with interval maps.

Autor: Valentin Deaconu, Fred Shultz

Publikováno v: Transactions of the American Mathematical Society; Mar2007, Vol. 359 Issue 4, p1889-1924, 36p

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