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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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Cited by 16 (4 self)
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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.
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.
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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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
Simulating Causal Collapse Models
, 2004
"... We present simulations of causal dynamical collapse models of field theories on a 1 + 1 null lattice. We use our simulations to compare and contrast two possible interpretations of the models, one in which the field values are real and the other in which the state vector is real. We suggest that a p ..."
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We present simulations of causal dynamical collapse models of field theories on a 1 + 1 null lattice. We use our simulations to compare and contrast two possible interpretations of the models, one in which the field values are real and the other in which the state vector is real. We suggest that a procedure of coarse graining and renormalising the fundamental field can overcome its noisiness and argue that this coarse grained renormalised field will show interesting structure if the state vector does on the coarse grained scale. a
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
Under consideration for publication in Math. Struct. in Comp. Science Quantum Programming Languages Survey and Bibliography
, 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. 1.
Using BV to Describe Causal Quantum Evolution
, 2004
"... this paper sequents should always be considered "up to permutation", i.e. one may rearrange the order of premises and conclusions as one sees fit. Our system will have only one inference rule, called the Cut rule,whichstates: #,A # # ,A# # # #,# # Axioms are of the form A 1 ,A 2 ,.. ..."
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this paper sequents should always be considered "up to permutation", i.e. one may rearrange the order of premises and conclusions as one sees fit. Our system will have only one inference rule, called the Cut rule,whichstates: #,A # # ,A# # # #,# # Axioms are of the form A 1 ,A 2 ,...,A n B 1 ,B 2 ,...,B m,w hereA 1 ,A 2 ,...,A n are the incoming edges of some vertex in our causal graph, and B 1 ,B 2 ,...,B m will be the outgoing edges. There will be one such axiom for each vertex. For example, consider Figure 3. Then we will have the following axioms: cb d, e, f c, d g, h e if,g jh,i k where we have labelled each entailment symbol with the name of the corresponding vertex. The following is an example of a deduction in this system of the sequent a, b f,g,h,i
Simulating Causal Wave Function Collapse Models
, 2004
"... We present simulations of causal dynamical wave function collapse models of field theories on a 1 + 1 null lattice. We use our simulations to compare and contrast two possible interpretations of the models, one in which the field values are real and the other in which the state vector is real. We su ..."
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We present simulations of causal dynamical wave function collapse models of field theories on a 1 + 1 null lattice. We use our simulations to compare and contrast two possible interpretations of the models, one in which the field values are real and the other in which the state vector is real. We suggest that a procedure of coarse graining and renormalising the fundamental field can overcome its noisiness and argue that this coarse grained renormalised field will show interesting structure if the state vector does on the coarse grained scale. We speculate on the implications for quantum gravity.