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Quantum Programming Languages  Survey and Bibliography
 UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
, 2006
"... The field of quantum programming languages is developing rapidly and there is a surprisingly large literature. Research in this area includes the design of programming languages for quantum computing, the application of established semantic and logical techniques to the foundations of quantum mechan ..."
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The field of quantum programming languages is developing rapidly and there is a surprisingly large literature. Research in this area includes the design of programming languages for quantum computing, the application of established semantic and logical techniques to the foundations of quantum mechanics, and the design of compilers for quantum programming languages. This article justifies the study of quantum programming languages, presents the basics of quantum computing, surveys the literature in quantum programming languages, and indicates directions for future research.
Physical traces: Quantum vs. classical information processing
 In Proceedings of Category Theory and Computer Science 2002 (CTCS’02), volume 69 of Electronic Notes in Theoretical Computer Science. Elsevier Science
, 2003
"... a setting that enables qualitative differences between classical and quantum processes to be explored. The key construction is the physical interpretation/realization of the traced monoidal categories of finitedimensional vector spaces with tensor product as monoidal structure and of finite sets an ..."
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a setting that enables qualitative differences between classical and quantum processes to be explored. The key construction is the physical interpretation/realization of the traced monoidal categories of finitedimensional vector spaces with tensor product as monoidal structure and of finite sets and relations with Cartesian product as monoidal structure, both of them providing a socalled wavestyle GoI. The developments in this paper reveal that envisioning state update due to quantum measurement as a process provides a powerful tool for developing highlevel approaches to quantum information processing.
Foliable operational structures for general probabilistic theories
 Deep Beauty: Understanding the Quantum World through Mathematical Innovation
, 2011
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The operator tensor formulation of quantum theory
 Arxiv:1201.4390 and Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
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Deep Inference and Probabilistic Coherence Spaces
, 2009
"... This paper proposes a definition of categorical model of the deep inference system BV, introduced by Guglielmi. Our definition is based on the notion of a linear functor, due to Cockett and Seely. A BVcategory is a linearly distributive category, possibly with negation, with an additional tensor pr ..."
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Cited by 4 (2 self)
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This paper proposes a definition of categorical model of the deep inference system BV, introduced by Guglielmi. Our definition is based on the notion of a linear functor, due to Cockett and Seely. A BVcategory is a linearly distributive category, possibly with negation, with an additional tensor product which, when viewed as a bivariant functor, is linear with a degeneracy condition. We show that this simple definition implies all of the key isomorphisms of the theory. We show that coherence spaces, with Retoré’s noncommutative tensor, is a model.We then consider Girard’s category of probabilistic coherence spaces and show that it contains a selfdual monoidal structure in addition to the ∗autonomous structure exhibited by Girard. This
A logical basis for quantum evolution and entanglement
, 2011
"... We reconsider discrete quantum casual dynamics where quantum systems are viewed as discrete structures, namely directed acyclic graphs. In such a graph, events are considered as vertices and edges depict propagation between events. Evolution is described as happening between a special family of spa ..."
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We reconsider discrete quantum casual dynamics where quantum systems are viewed as discrete structures, namely directed acyclic graphs. In such a graph, events are considered as vertices and edges depict propagation between events. Evolution is described as happening between a special family of spacelike slices, which were referred to as locative slices. Such slices are not so large as to result in acausal influences, but large enough to capture nonlocal correlations. In our logical interpretation, edges are assigned logical formulas in a special logical system, called BV, an instance of a deep inference system. We demonstrate that BV, with its mix of commutative and noncommutative connectives, is precisely the right logic for such analysis. We show that the commutative tensor encodes (possible) entanglement, and the noncommutative seq encodes causal precedence. With this interpretation, the locative slices are precisely the derivable strings of formulas.
Theoryindependent limits on correlations from generalised Bayesian networks
"... Bayesian networks provide a powerful tool for reasoning about probabilistic causation, used in many areas of science. They are, however, intrinsically classical. In particular, Bayesian networks naturally yield the Bell inequalities. Inspired by this connection, we generalise the formalism of class ..."
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Bayesian networks provide a powerful tool for reasoning about probabilistic causation, used in many areas of science. They are, however, intrinsically classical. In particular, Bayesian networks naturally yield the Bell inequalities. Inspired by this connection, we generalise the formalism of classical Bayesian networks in order to investigate nonclassical correlations in arbitrary causal structures. Our framework of ‘generalised Bayesian networks ’ replaces latent variables with the resources of any generalised probabilistic theory, most importantly quantum theory, but also, for example, PopescuRohrlich boxes. We obtain three main sets of results. Firstly, we prove that all of the observable conditional independences required by the classical theory also hold in our generalisation; to obtain this, we extend the classical dseparation theorem to our setting. Secondly, we find that the theoryindependent constraints on probabilities can go beyond these conditional independences. For example we find that no probabilistic theory predicts perfect correlation between three parties using only bipartite common causes. Finally, we begin a classification of those causal structures, such as the Bell scenario, that may yield a separation between classical, quantum and generalprobabilistic correlations. 1
September 12, 2008 — Submitted to Trends in Logic VI The Logic BV and Quantum Causality
"... We describe how a logic with commutative and noncommutative connectives can be used for capturing the essence of discrete quantum causal propagation. 1 Causal graphs and locative slices In this note we describe how the kinematics of quantum causal evolution can be captured by the logic BV [2]. The s ..."
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We describe how a logic with commutative and noncommutative connectives can be used for capturing the essence of discrete quantum causal propagation. 1 Causal graphs and locative slices In this note we describe how the kinematics of quantum causal evolution can be captured by the logic BV [2]. The setting is discrete quantum mechanics. We imagine a finite “web ” of spacetime points. They are viewed as vertices in a directed acyclic graph (DAG); the edges of the DAG represent causal links mediated by the propagation of matter [1]. The fact that the graph is acyclic captures a basic causality requirement: there are no closed causal trajectories. The DAG represents a discrete approximation to the spacetime on which a quantum system evolves. The graph