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Non-Commutative Topology for Curved Quantum Causality [article]

Ioannis Raptis
2001 arXiv   pre-print
We compare our non-commutative scheme-theoretic curved quantum causal topology with some recent C^*-quantale models for non-abelian generalizations of classical commutative topological spaces or locales  ...  This is modeled after a non-commutative scheme type of theory for the curved finitary spacetime sheaves of the non-abelian incidence Rota algebras that represent 'gravitational quantum causal sets'.  ...  On the other hand, as Butterfield et al. (2000) remarked in constructing the spectra for the commutative * -algebras V in V, if non-commutative C * -algebras N were used as objects in the base category  ... 
arXiv:gr-qc/0101082v2 fatcat:sgjamt73u5g7dm7jnb7ndvgt5y

Non-unitary Evolution of Quantum Logics [chapter]

Sebastian Fortin, Federico Holik, Leonardo Vanni
2016 Springer Proceedings in Physics  
We present some simple models which illustrate this transition and develop a new quantum logical formalism based in complex spectral resolutions, a notion that we introduce in order to cope with the temporal  ...  By changing the standard formalism of quantum mechanics to allow non-Hermitian operators as generators of time evolution, we address the question of how can logics evolve in time.  ...  On the other hand, for classical systems, onservables are represented by functions over phase space and form a commutative algebra; thus, classical properties are distributive [20, 23] .  ... 
doi:10.1007/978-3-319-31356-6_14 fatcat:vmjwwgpzkja6jnw65x4o2hxql4

Specifying and Verifying Communications Protocols using Mixed Intuitionistic Linear Logic

David Sinclair, James Power
2005 Electronical Notes in Theoretical Computer Science  
The logical formalism used is Mixed Intuitionistic Linear Logic in order to use both commutative and noncommutative operators to model the concurrent and sequential processes in these protocols.  ...  In this paper we present a technique for specifying and verifying communications protocols and demonstrate this approach by specifying and verifying two of the fundamental communications protocols, namely  ...  Acknowledgement The authors would like to thank the anonymous reviewrs for their helpful comments and suggestions.  ... 
doi:10.1016/j.entcs.2004.08.068 fatcat:llttwuw2xjbobetkolgxbq5dxm

Superlogic Manifolds and Geometric approach to Quantum Logic [article]

Joseph Kouneiher, Newton Da Costa
2015 arXiv   pre-print
Note that this superlogic is not distributive reflecting a good propriety to describe quantum mechanics, non commutative spaces and contains a nilpotent element.  ...  This approach constitutes a new way of looking at the connection between quantum mechanics and logic. It is a geometrisation of the quantum logic.  ...  as basic models for the logics affiliated with physical systems.  ... 
arXiv:1505.00756v2 fatcat:hwqzvkf5hnguraceomrkn2jige

Quasiparticle Localisation via Frequent Measurements [article]

David Herrera-Martí, Ying Li, Leong Chuan Kwek
2013 arXiv   pre-print
However the logical operators commute with the measurement operators and are thus protected.  ...  We address this issue for a topological subsystem code introduced in [Bravyi S. et al., Quant.Inf.Comp.13(11):0963].  ...  Logical operators, on the other hand, commute with all the measurement operators, and will be conserved.  ... 
arXiv:1309.7718v1 fatcat:xfymjhfivjedtp5lbl7mbl3gc4

A Conceptual Construction of Complexity Levels Theory in Spacetime Categorical Ontology: Non-Abelian Algebraic Topology, Many-Valued Logics and Dynamic Systems

R. Brown, J. F. Glazebrook, I. C. Baianu
2007 Axiomathes  
as well as to derive novel results for (non-commutative) Quantum Logics.  ...  algebraic topology (NAAT) Á Non-commutativity of diagrams and non-Abelian theories-Non-Abelian categorical ontology Á Non-commutative topological invariants of complex dynamic state spaces Á Natural transformations  ...  , especially a complete, non-commutative theory of levels founded in LM-and Q-logics. • The potential now exists for exact, symbolic calculation of the non-commutative invariants of spacetime through logical  ... 
doi:10.1007/s10516-007-9010-3 fatcat:246y6llurzhi5mwyofr373rxvm

Quantum Fermi's Golden Rule [article]

Fausto Rossi
2007 arXiv   pre-print
In particular, we shall show that -contrary to the semiclassical case- the Markov limit does not preserve the positive-definite character of the corresponding density matrix, thus leading to highly non-physical  ...  For purely atomic and/or photonic quantum logic gates, decoherence phenomena are successfully described via adiabatic-decoupling procedures [10] in terms of extremely simplified models via phenomenological  ...  structure in (3) describes, in general, a non-reversible (i.e., non unitary) dynamics characterized by energy dissipation and dephasing.  ... 
arXiv:quant-ph/0702233v1 fatcat:4zra7t5a5rgflfl7za4qncjeqm

Inductive logic: from data analysis to experimental design

Kevin H. Knuth
2002 AIP Conference Proceedings  
In this exploration we demonstrate that the duality between the logic of assertions and the logic of questions has important consequences.  ...  In celebration of the work of Richard Threlkeld Cox, we explore inductive logic and its role in science touching on both experimental design and analysis of experimental results.  ...  Application of the same procedure to (17), equating the right-hand sides and solving for H(b | c) gives FIGURE 1 . 1 Venn diagrams demonstrating the symmetries between (a) the logic of assertions and  ... 
doi:10.1063/1.1477061 fatcat:5mq3w7pcrve6fbq2v5crsdjfwm

Majorana fermion codes

Sergey Bravyi, Barbara M Terhal, Bernhard Leemhuis
2010 New Journal of Physics  
These codes can be viewed as extensions of Kitaev's 1D model of unpaired Majorana fermions in quantum wires to higher spatial dimensions and interacting fermions.  ...  An essential part of the model is that the only even-weight logical operator c 1 c 2L is very non-local.  ...  The weakly self-dual character of the CSS code, or the fact that the Hamiltonian of the Z 2 -gauge model has only terms with even overlap, is crucial.  ... 
doi:10.1088/1367-2630/12/8/083039 fatcat:smvd2g3icvgdthpnzwrseplurq

Around logical perfection [article]

John Alexander Cruz Morales, Andrés Villaveces, Boris Zilber
2019 arXiv   pre-print
In this article we present and describe a notion of "logical perfection". We extract the notion of "perfection" from the contemporary logical concept of categoricity.  ...  We postulate and present the category of logical perfection.  ...  In non-commutative cases the situation becomes much more complex but model theory is in the best position to deal with the challenge.  ... 
arXiv:1803.04909v2 fatcat:gmd4giuiazhmni7jet36is3yta

A theory of effects and resources: adjunction models and polarised calculi

Pierre-Louis Curien, Marcelo Fiore, Guillaume Munch-Maccagnoni
2016 SIGPLAN notices  
point for a comprehensive semantic theory relating logical systems, typed calculi, and categorical models in this context.  ...  extension of linear/non-linear adjunction models with an adjoint resolution of computational effects.  ...  There, categorical models of linear logic are built from polarised ones by enforcing commutativity of the strong monad ¬¬.  ... 
doi:10.1145/2914770.2837652 fatcat:xxsp3hzef5h3pedlklh5dcawzm

A theory of effects and resources: adjunction models and polarised calculi

Pierre-Louis Curien, Marcelo Fiore, Guillaume Munch-Maccagnoni
2016 Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL 2016  
point for a comprehensive semantic theory relating logical systems, typed calculi, and categorical models in this context.  ...  extension of linear/non-linear adjunction models with an adjoint resolution of computational effects.  ...  There, categorical models of linear logic are built from polarised ones by enforcing commutativity of the strong monad ¬¬.  ... 
doi:10.1145/2837614.2837652 dblp:conf/popl/CurienFM16 fatcat:hboqbuhw2nehpizlekkhjvaidu

Overturning negative construal of quantum superposition [article]

Arkady Bolotin
2021 arXiv   pre-print
(like general relativity or quantum mechanics), but also on a mathematical model of reasoning used to analyze and appraise statements regarding the objective world (for example, logic of one type or the  ...  However, since none of the extra postulates proposed so far has gained broad acceptance, one may try another avenue to resolve the problem, namely, to replace logic with an alternative mathematical model  ...  of purely logical character determined from logic alone.  ... 
arXiv:2107.07989v1 fatcat:suytnauol5fx3g7rewow7y4odq

Modelling and querying interaction networks in the biochemical abstract machine BIOCHAM

F Fages
2002 Journal of Biological Physics and Chemistry  
In this article we present a formal modelling environment for network biology, called the Biochemical Abstract Machine (BIOCHAM). Biocham delivers precise semantics to biomolecular interaction maps.  ...  We present the main features of Biocham and report on our modelling experience with this language.  ...  CTL basically extends propositional logic used for describing states, with operators for reasoning over time and non-determinism.  ... 
doi:10.4024/2040402.jbpc.04.02 fatcat:lqy66ssppnaohjd2f6ggdfxtsu

Categorical Ontology of Complex Spacetime Structures: The Emergence of Life and Human Consciousness

I. C. Baianu, R. Brown, J. F. Glazebrook
2007 Axiomathes  
with those obtained for (non-commutative) quantum logics.  ...  , LM-and Q-logic Á Organismic categories and relational patterns Á Abelian vs. non-Abelian theories Á Commutativity limitations in logics, mathematics, physics and emergent systems Á Łukasiewicz-Moisil  ...  (non-commutative) Łukasiewicz-Moisil logics.  ... 
doi:10.1007/s10516-007-9011-2 fatcat:m3kuram2fjcwze4mkmfxk2akwu
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