75 citations · 544 across the 41 of their papers we have counts for
6 papers · 1 filter
A 2-Categorical Analysis of Complementary Families, Quantum Key Distribution and the Mean King Problem
Krzysztof Bar, Jamie Vicary
This paper explores the use of 2-categorical technology for describing and reasoning about complex quantum procedures. We give syntactic definitions of a family of complementary me…
Extended 3-dimensional bordism as the theory of modular objects
Bruce Bartlett, Christopher L. Douglas, Christopher J. Schommer-Pries +1
A modular object in a symmetric monoidal bicategory is a Frobenius algebra object whose product and coproduct are biadjoint, equipped with a braided structure and a compatible twis…
Abstract structure of unitary oracles for quantum algorithms
William Zeng, Jamie Vicary
We show that a pair of complementary dagger-Frobenius algebras, equipped with a self-conjugate comonoid homomorphism onto one of the algebras, produce a nontrivial unitary morphism…
Mixed quantum states in higher categories
Chris Heunen, Jamie Vicary, Linde Wester
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…
Wormholes and Entanglement
John C. Baez, Jamie Vicary
Maldacena and Susskind have proposed a correspondence between wormholes and entanglement, dubbed ER=EPR. We study this in the context of 3d topological quantum field theory, where…
Groupoid Semantics for Thermal Computing
Krzysztof Bar, Jamie Vicary
A groupoid semantics is presented for systems with both logical and thermal degrees of freedom. We apply this to a syntactic model for encryption, and obtain an algebraic character…