Results 51 to 60 of about 470,444 (191)
Completely positive maps of order zero on pro-𝐶∗-algebras
, 2020 We extend the definition of order zero maps to the setting of pro-C*{C^{*}}-algebras and generalize structure theorems of order zero maps between C*{C^{*}}-algebras to strongly bounded order zero maps between pro-C∗{C^{\ast}}-algebras.
M. Joita
semanticscholar +1 more source
Faster Together: Collective Quantum Search
Entropy, 2015 Joining independent quantum searches provides novel collective modes of quantum search (merging) by utilizing the algorithm’s underlying algebraic structure.
Demosthenes Ellinas +1 more
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Axiomatizing complete positivity [PDF]
Electronic Proceedings in Theoretical Computer Science, 2015 There are two ways to turn a categorical model for pure quantum theory into one for mixed quantum theory, both resulting in a category of completely positive maps.
Oscar Cunningham, Chris Heunen
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Mixed quantum states in higher categories [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 There are two ways to describe the interaction between classical and quantum information categorically: one based on completely positive maps between Frobenius algebras, the other using symmetric monoidal 2-categories.
Chris Heunen, Jamie Vicary, Linde Wester
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Interpolation by completely positive maps [PDF]
Linear and Multilinear Algebra, 2011 Given commuting families of Hermitian matrices {A 1, … , A k } and {B 1, … , B k }, conditions for the existence of a completely positive map Φ, such that Φ(A j ) = B j for j = 1, … , k, are studied. Additional properties such as unital or/and trace preserving on the map Φ are also considered.
Chi-Kwong Li, Yiu-Tung Poon
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Infinite dimensional generalizations of Choi’s Theorem
Special Matrices, 2019 In this paper we give a simple sequence of necessary and sufficient finite dimensional conditions for a positive map between certain subspaces of bounded linear operators on separable Hilbert spaces to be completely positive. These criterions are natural
Friedland Shmuel
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Two Roads to Classicality [PDF]
Electronic Proceedings in Theoretical Computer Science, 2018 Mixing and decoherence are both manifestations of classicality within quantum theory, each of which admit a very general category-theoretic construction. We show under which conditions these two 'roads to classicality' coincide.
Bob Coecke, John Selby, Sean Tull
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Categories of relations as models of quantum theory [PDF]
Electronic Proceedings in Theoretical Computer Science, 2015 Categories of relations over a regular category form a family of models of quantum theory. Using regular logic, many properties of relations over sets lift to these models, including the correspondence between Frobenius structures and internal groupoids.
Chris Heunen, Sean Tull
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Characterization of the order relation on the set of completely n-positive linear maps between C*-algebras [PDF]
Surveys in Mathematics and its Applications, 2007 In this paper we characterize the order relation on the set of all nondegenerate completely n-positive linear maps between C*-algebras in terms of a self-dual Hilbert module induced by each completely n-positive linear map.
Maria Joita +2 more
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Semantics for a Quantum Programming Language by Operator Algebras [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 This paper presents a novel semantics for a quantum programming language by operator algebras, which are known to give a formulation for quantum theory that is alternative to the one by Hilbert spaces.
Kenta Cho
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