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A categorical semantics of quantum protocols
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 willExpand
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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 areaExpand
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Mathematical Foundations for 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, for which we rely onExpand
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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 generalExpand
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A categorical semantics of quantum protocols
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 willExpand
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Categorical quantum mechanics
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 theExpand
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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 quantumExpand
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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-dimensionalExpand
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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’sExpand
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The Compositional Structure of Multipartite Quantum Entanglement
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 isExpand
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