5 research outputs found
Groupoid Semantics for Thermal Computing
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 characterization of the heat produced by the encryption
function, as predicted by Landauer's principle. Our model has a linear
representation theory that reveals an underlying quantum semantics, giving for
the first time a functorial classical model for quantum teleportation and other
quantum phenomena.Comment: We describe a groupoid model for thermodynamic computation, and a
quantization procedure that turns encrypted communication into quantum
teleportation. Everything is done using higher category theor
A 2-Categorical Analysis of Complementary Families, Quantum Key Distribution and the Mean King Problem
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 measurements, and of quantum key distribution, and show
that they are equivalent. We then show abstractly that either structure gives a
solution to the Mean King problem, which we also formulate 2-categorically.Comment: In Proceedings QPL 2014, arXiv:1412.810
Mixed quantum states in higher categories
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. This paper
makes a first step towards combining the two. The integrated approach allows a
unified description of quantum teleportation and classical encryption in a
single 2-category, as well as a universal security proof applicable
simultaneously to both scenarios.Comment: In Proceedings QPL 2014, arXiv:1412.810
A classical groupoid model for quantum networks
We give a mathematical analysis of a new type of classical computer network
architecture, intended as a model of a new technology that has recently been
proposed in industry. Our approach is based on groubits, generalizations of
classical bits based on groupoids. This network architecture allows the direct
execution of a number of protocols that are usually associated with quantum
networks, including teleportation, dense coding and secure key distribution
A Classical Groupoid Model for Quantum Networks
We give a mathematical analysis of a new type of classical computer network architecture, intended as a model of a new technology that has recently been proposed in industry. Our approach is based on groubits, generalizations of classical bits based on groupoids. This network architecture allows the direct execution of a number of protocols that are usually associated with quantum networks, including teleportation, dense coding and secure key distribution