Categorical quantum mechanics

  title={Categorical quantum mechanics},
  author={Samson Abramsky and Bob Coecke},
  journal={arXiv: Quantum Physics},
Braided Categorical Quantum Mechanics I
This is the first paper in a series where the Categorical Quantum Mechanics program is generalized to braided systems and category theory is used to construct a high-level language that describes the role of quantum information in these systems.
Environment and Classical Channels in Categorical Quantum Mechanics
We present a both simple and comprehensive graphical calculus for quantum computing. We axiomatize the notion of an environment, which together with the axiomatic notion of classical structure
Higher Quantum Theory
The 2-categorical formalism gives a simple, graphical way to describe the specification and implementation of certain quantum procedures, which is used to investigate quantum teleportation, dense coding, complementarity and quantum erasure.
Diagrammatic quantum mechanics
This paper explores how diagrams of quantum processes can be used for modeling and for quantum epistemology. The paper is a continuation of the discussion where we began this formulation. Here we
A Note on the "Third Life of Quantum Logic"
The purpose of this note is to discuss some of the questions raised by Dunn, J. Michael; Moss, Lawrence S.; Wang, Zhenghan in Editors' introduction: the third life of quantum logic: quantum logic
Category Theory and Quantum Mechanics
  • G. Auletta
  • Philosophy
    The Quantum Mechanics Conundrum
  • 2019
In the present chapter, the general logical–epistemological foundations of the quantum theory, where the stress is on categorisation are dealt with, and its applications to QM and especially to quantum information are seen.
Higher Semantics of Quantum Protocols
  • Jamie Vicary
  • Computer Science
    2012 27th Annual IEEE Symposium on Logic in Computer Science
  • 2012
A higher semantics for the description of quantum protocols is proposed, which deals with quantum and classical information in a unified way and uses the use of 2-category theory to formalize the resulting framework.
Se p 20 17 S-matrix Interpretation in Categorical Quantum Mechanics
We study the S-matrix interpretation of quantum theory in light of Categotical Quantum Mechanics. The S-matrix interpretation of quantum theory is shown to be a functorial semantics relating the
Effectuses in Categorical Quantum Foundations
This thesis develops the theory of effectuses as a categorical axiomatic approach to quantum theory. It provides a comprehensive introduction to effectus theory and reveals its connections with
The Sheaf-Theoretic Structure of Definite Causality
Also in the quantum theory one starts from certain numbers from which one deduces other numbers, which can be taken as initial numbers for a calculation in quantum theory.


Quantum computation and quantum information
  • T. Paul
  • Physics
    Mathematical Structures in Computer Science
  • 2007
This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing. The first two papers deal
A one-way quantum computer.
A scheme of quantum computation that consists entirely of one-qubit measurements on a particular class of entangled states, the cluster states, which are thus one-way quantum computers and the measurements form the program.
The Quantum Theory
IN a lecture on the quantum theory it might be thought fitting to commence with a clear explanation of the purpose, nature, and scope of the subject; but an attempt to answer briefly the question,
On the Foundations of Quantum Physics
The interpretation of quantum theory has always been a source of difficulties, especially with regard to the theory of measurement. We do not intend to enter here into the details of the polemic
A categorical semantics of quantum protocols
  • S. Abramsky, B. Coecke
  • Computer Science
    Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.
  • 2004
This paper focuses on quantum information protocols, which exploit quantum-mechanical effects in an essential way and form the basis for novel and potentially very important applications to secure and fault-tolerant communication and computation.
Quantum Teleportation is a Universal Computational Primitive
We present a method to create a variety of interesting gates by teleporting quantum bits through special entangled states. This allows, for instance, the construction of a quantum computer based on
The Logic of Quantum Mechanics
One of the aspects of quantum theory which has attracted the most general attention, is the novelty of the logical notions which it presupposes. It asserts that even a complete mathematical
Quantum computational networks
  • D. Deutsch
  • Physics, Computer Science
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1989
The theory of quantum computational networks is the quantum generalization of the theory of logic circuits used in classical computing machines, and a single type of gate, the universal quantum gate, together with quantum ‘unit wires' is adequate for constructing networks with any possible quantum computational property.
Categorical Geometry and the Mathematical Foundations of Quantum General Relativity
We explore the possibility of replacing point set topology by higher category theory and topos theory as the foundation for quantum general relativity. We discuss the BC model and problems of its
Quantum Computation, Categorical Semantics and Linear Logic
A type theory and denotational semantics are developed and provided for a simple fragment of the quantum lambda calculus, a formal language for quantum computation based on linear logic.