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Universal Properties in Quantum Theory [PDF]
Electronic Proceedings in Theoretical Computer Science, 2019 We argue that notions in quantum theory should have universal properties in the sense of category theory. We consider the completely positive trace preserving (CPTP) maps, the basic notion of quantum channel.
Mathieu Huot, Sam Staton
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Pictures of complete positivity in arbitrary dimension [PDF]
Electronic Proceedings in Theoretical Computer Science, 2012 Two fundamental contributions to categorical quantum mechanics are presented. First, we generalize the CP-construction, that turns any dagger compact category into one with completely positive maps, to arbitrary dimension.
Bob Coecke, Chris Heunen
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Bloch equations and completely positive maps [PDF]
Journal of Modern Optics, 2004 The phenomenological dissipation of the Bloch equations is reexamined in the context of completely positive maps. Such maps occur if the dissipation arises from a reduction of a unitary evolution of a system coupled to a reservoir. In such a case the reduced dynamics for the system alone will always yield completely positive maps of the density ...
Daffer, Sonja +2 more
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Completely positive classical structures and sequentializable quantum protocols [PDF]
Electronic Proceedings in Theoretical Computer Science, 2012 We study classical structures in various categories of completely positive morphisms: on sets and relations, on cobordisms, on a free dagger compact category, and on Hilbert spaces.
Chris Heunen, Sergio Boixo
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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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Causality and the complete positivity of classical polarization maps [PDF]
Optics Letters, 2011 Mueller and Jones matrices have been thoroughly studied as mathematical tools to describe the manipulation of the polarization state of classical light. In particular, the most general physical transformation on the polarization state has been represented as an ensemble of Jones matrices, as ∑iV(i)ΦV(i)(†).
Omar, Gamel, Daniel F V, James
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Entanglement-breaking superchannels [PDF]
Quantum, 2020 In this paper we initiate the study of entanglement-breaking (EB) superchannels. These are processes that always yield separable maps when acting on one side of a bipartite completely positive (CP) map.
Senrui Chen, Eric Chitambar
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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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