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A categorical semantics of quantum protocols
  • S. Abramsky, B. Coecke
  • Computer Science
    Proceedings of the 19th Annual IEEE Symposium on…
  • 18 February 2004
TLDR
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.
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Interacting quantum observables: categorical algebra and diagrammatics
TLDR
The ZX-calculus is introduced, an intuitive and universal graphical calculus for multi-qubit systems, which greatly simplifies derivations in the area of quantum computation and information and axiomatize phase shifts within this framework.
View on IOP Publishing
Mathematical Foundations for a Compositional Distributional Model of Meaning
TLDR
A mathematical framework for a unification of the distributional theory of meaning in terms of vector space models and a compositional theory for grammatical types, for which the type reductions of Pregroups are lifted to morphisms in a category, a procedure that transforms meanings of constituents into a meaning of the (well-typed) whole.
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Interacting Quantum Observables
TLDR
Using a general categorical formulation, it is shown that pairs of mutually unbiased quantum observables form bialgebra-like structures that enable all observables of finite dimensional Hilbert space quantum mechanics to be described.
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Categorical quantum mechanics
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Picturing Quantum Processes
Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning
TLDR
This entirely diagrammatic presentation of quantum theory represents the culmination of ten years of research, uniting classical techniques in linear algebra and Hilbert spaces with cutting-edge developments in quantum computation and foundations.
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Quantum measurements without sums
Sums play a prominent role in the formalisms of quantum me- chanics, whether for mixing and superposing states, or for composing state spaces. Surprisingly, a conceptual analysis of quantum…
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A Compositional Distributional Model of Meaning
We propose a mathematical framework for a unification of the distributional theory of meaning in terms of vector space models, and a compositional theory for grammatical types, namely Lambek’s…
A new description of orthogonal bases
We show that an orthogonal basis for a finite-dimensional Hilbert space can be equivalently characterised as a commutative †-Frobenius monoid in the category FdHilb, which has finite-dimensional…
View on Cambridge Press
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