Categorical quantum mechanics

@article{Abramsky2008CategoricalQM,
  title={Categorical quantum mechanics},
  author={Samson Abramsky and Bob Coecke},
  journal={arXiv: Quantum Physics},
  year={2008}
}
Braided Categorical Quantum Mechanics I
TLDR
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.
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We present a both simple and comprehensive graphical calculus for quantum computing. In particular, we axiomatize the notion of an environment, which together with the earlier introduced axiomatic
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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.
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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
Higher Semantics of Quantum Protocols
  • Jamie Vicary
  • Computer Science
    2012 27th Annual IEEE Symposium on Logic in Computer Science
  • 2012
TLDR
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.
Category Theory and Quantum Mechanics
  • G. Auletta
  • Philosophy
    The Quantum Mechanics Conundrum
  • 2019
TLDR
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.
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
  • S. Gogioso, N. Pinzani
  • Physics, Philosophy
    Electronic Proceedings in Theoretical Computer Science
  • 2021
TLDR
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.
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