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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 pregroup semantics. A key observation is that the monoidal category of (finite dimensional) vector spaces, ..."
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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 pregroup semantics. A key observation is that the monoidal category of (finite dimensional) vector spaces, linear maps and the tensor product, as well as any pregroup, are examples of compact closed categories. Since, by definition, a pregroup is a compact closed category with trivial morphisms, its compositional content is reflected within the compositional structure of any nondegenerate compact
Kindergarten quantum mechanics — lecture notes
 In: Quantum Theory: Reconsiderations of the Foundations III
, 2005
"... Abstract. These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns ‘doing quantum mechanics using only pictures of lines, squares, triangles and diamonds’. This picture calculus can be seen as a very substanti ..."
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Abstract. These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns ‘doing quantum mechanics using only pictures of lines, squares, triangles and diamonds’. This picture calculus can be seen as a very substantial extension of Dirac’s notation, and has a purely algebraic counterpart in terms of socalled Strongly Compact Closed Categories (introduced by Abramsky and I in [3, 4]) which subsumes my Logic of Entanglement [11]. For a survey on the ‘what’, the ‘why ’ and the ‘hows ’ I refer to a previous set of lecture notes [12, 13]. In a last section we provide some pointers to the body of technical literature on the subject.
Quantum Programming Languages: An Introductory Overview
, 2006
"... The present article gives an introductory overview of the novel field of quantum programming languages (QPLs) from a pragmatic perspective. First, after a short summary of basic notations of quantum mechanics, some of the goals and design issues are surveyed, which motivate the research in this area ..."
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The present article gives an introductory overview of the novel field of quantum programming languages (QPLs) from a pragmatic perspective. First, after a short summary of basic notations of quantum mechanics, some of the goals and design issues are surveyed, which motivate the research in this area. Then, several of the approaches are described in more detail. The article concludes with a brief survey of current research activities and a tabular summary of a selection of QPLs, which have been published so far.
ON THE ARROW OF TIME
, 708
"... Abstract. The interface between classical physics and quantum physics is explained from the point of view of Quantum Information Theory (Feynman Processes), based on the qubit model. The interpretation depends on a hefty sacrifice: the classical determinism or the arrow of time. As a benefit, the wa ..."
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Abstract. The interface between classical physics and quantum physics is explained from the point of view of Quantum Information Theory (Feynman Processes), based on the qubit model. The interpretation depends on a hefty sacrifice: the classical determinism or the arrow of time. As a benefit, the waveparticle duality naturally emerges from the qubit model, as the root of creation and annihilation of possibilities (quantum logic). A few key experiments are briefly reviewed from the above perspective: quantum erasure, delayedchoice and waveparticle correlation. The CPTTheorem is interpreted in the framework of categories with duality and a timeless interpretation of the Feynman Processes is proposed. A connection between the finestructure constant and algebraic number theory is
Teleportation, Braid Group and Temperley–Lieb Algebra”, quantph/0601050
 23 George Svetlichny, Foundations of Physics
, 1981
"... ..."
Tensor universality, quantum information flow, Coecke’s theorem, and generalizations
 Unpublised
"... We show that Coecke’s compositionality theorem for quantum information flow follows by the universal property of tensor products from the case in which all relevant states are totally disentangled, for which the proof is almost trivial. With the same technique we deduce a PROP structure behind gener ..."
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We show that Coecke’s compositionality theorem for quantum information flow follows by the universal property of tensor products from the case in which all relevant states are totally disentangled, for which the proof is almost trivial. With the same technique we deduce a PROP structure behind general multipartite quantum information processing and show that all such are equivalent to a canonical teleportationtype form. Some philosophical issues concerning quantum information are also touched upon. 1
Physics from Computer Science — a position statement —
, 2006
"... In this statement we provide some examples of transdisciplinary journeys, from one field to another, and back. In particular, the quantum informatic endeavor is not just a matter of feeding physical theory into the general field of natural computation, but also one of using highlevel methods develo ..."
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In this statement we provide some examples of transdisciplinary journeys, from one field to another, and back. In particular, the quantum informatic endeavor is not just a matter of feeding physical theory into the general field of natural computation, but also one of using highlevel methods developed in Computer Science to improve on the quantum physical formalism itself, and the understanding thereof. We highlight a seemingly contradictory phenomenon: passing to an abstract, categorical quantum informatic formalism leads directly to a simple and elegant graphical formulation of quantum theory itself, which for example makes the design of some important quantum informatic protocols completely transparent. It turns out that essentially all of the quantum informatic machinery can be recovered from this graphical calculus. But in turn, this graphical formalism provides a bridge between methods of logic and computer science, and some of the most exciting developments in the mathematics of the past two decades: namely those arising from the Jones polynomial invariant of knots and links, the TemperleyLieb Algebra and related structures.