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A categorical semantics of quantum protocols

- Samson Abramsky, B. Coecke
- Computer Science, Physics
- Proceedings of the 19th Annual IEEE Symposium on…
- 18 February 2004

Particular focus in this paper is on quantum information protocols, which exploit quantum-mechanical effects in an essential way. The particular examples we shall use to illustrate our approach will… Expand

Interacting Quantum Observables: Categorical Algebra and Diagrammatics

This paper has two tightly intertwined aims: (i) to introduce an intuitive and universal graphical calculus for multi-qubit systems, the ZX-calculus, which greatly simplifies derivations in the area… Expand

Mathematical Foundations for a Compositional Distributional Model of Meaning

- B. Coecke, M. Sadrzadeh, Stephen Clark
- Computer Science, Mathematics
- ArXiv
- 1 March 2010

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, for which we rely on… Expand

Interacting Quantum Observables

We formalise the constructive content of an essential feature of quantum mechanics: the interaction of complementary quantum observables, and information flow mediated by them. Using a general… Expand

A categorical semantics of quantum protocols

- Samson Abramsky, B. Coecke
- Computer Science
- LICS
- 13 July 2004

Particular focus in this paper is on quantum information protocols, which exploit quantum-mechanical effects in an essential way. The particular examples we shall use to illustrate our approach will… Expand

Categorical quantum mechanics

- Samson Abramsky, B. Coecke
- Physics, Mathematics
- 7 August 2008

This invited chapter in the Handbook of Quantum Logic and Quantum Structures consists of two parts: 1. A substantially updated version of quant-ph/0402130 by the same authors, which initiated the… Expand

Quantum measurements without sums

- B. Coecke, Dusko Pavlovic
- Mathematics, Physics
- 3 August 2006

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… Expand

A new description of orthogonal bases

- B. Coecke, Dusko Pavlovic, Jamie Vicary
- Physics, Mathematics
- Math. Struct. Comput. Sci.
- 5 October 2008

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… Expand

A Compositional Distributional Model of Meaning

- Stephen Clark, B. Coecke, Mehrnoosh
- 2008

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… Expand

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The Compositional Structure of Multipartite Quantum Entanglement

- B. Coecke, A. Kissinger
- Computer Science, Mathematics
- ICALP
- 12 February 2010

Multipartite quantum states constitute a (if not the) key resource for quantum computations and protocols. However obtaining a generic, structural understanding of entanglement in N-qubit systems is… Expand