153 research outputs found
On some properties of quasi-MV algebras and square root quasi-MV algebras. Part II
No full textThe present paper is a sequel to Paoli F, Ledda A, Giuntini R, Freytes H (On some properties of QMV algebras and root'QMV algebras, submitted). We provide two representation results for quasi-MV algebras in terms of MV algebras enriched with additional structure; we investigate the lattices of subvarieties and subquasivarieties of quasi-MV algebras; we show that quasi-MV algebras, as well as cartesian and flat root' quasi-MV algebras, have the amalgamation propert
Interpreting the Modal Kochen-Specker Theorem: Possibility and Many Worlds in Quantum Mechanics
No full textIn this paper we attempt to physically interpret the Modal Kochen-Specker (MKS) theorem. In order to do so, we analyze the features of the possible properties about quantum systems arising from the elements in an orthomodular lattice and distinguish the use of “possibility” in the classical and quantum formalisms. Taking into account the modal and many worlds non-collapse interpretation of the projection postulate, we discuss how the MKS theorem rules the constrains to actualization, and thus, the relation between actual and possible realms
Lógicas multivaluadas y la axiomatización de la lógica computacional cuántica
No full textFil: Domenech, G. Universidad de Buenos Aires; Argentina.Fil: Domenech, G. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Astronomía y Física del Espacio; Argentina.Fil: Freytes, H. Universidad Nacional de Rosario. Facultad de Humanidades y Arte. Escuela de Filosofía; Argentina.El significado de una sentencia elemental en la lógica asociada a la computación cuántica está representado por la cantidad de información cuántica codificada en una colección de qbits, el equivalente cuántico de los bits clásicos (0, 1 o F, V), o de qmixesFil: Domenech, G. Universidad de Buenos Aires; Argentina.Fil: Domenech, G. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Astronomía y Física del Espacio; Argentina.Fil: Freytes, H. Universidad Nacional de Rosario. Facultad de Humanidades y Arte. Escuela de Filosofía; Argentina
Many worlds and modality in the interpretation of quantum mechanics: an algebraic approach
No full textMany worlds interpretations (MWI) of quantum mechanics avoid the measurement problem by considering every term in the quantum superposition as actual. A seemingly opposed solution is proposed by modal interpretations (MI) which state that quantum mechanics does not provide an account of what ?actually is the case?, but rather deals with what ?might be the case?, i.e. with possibilities. In this paper we provide an algebraic framework which allows us to analyze in depth the modal aspects of MWI. Within our general formal scheme we also provide a formal comparison between MWI and MI, in particular, we provide a formal understanding of why ?even though both interpretations share the same formal structure? MI fall pray of Kochen-Specker (KS) type contradictions while MWI escape them.Fil: Domenech, Graciela. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; ArgentinaFil: Freytes Solari, Hector Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universita degli Studi di Cagliari; ItaliaFil: de Ronde, Christian. Vrije Unviversiteit Brussel; Bélgica. Universidad de Buenos Aires. Facultad de Filosofía y Letras. Instituto de Filosofía "Dr. Alejandro Korn"; Argentin
Quantum probability: a reliable tool for an agent or a reliable source of reality?
No full textIn this paper we attempt to analyze the concept of quantum probability within quantum computation and quantum computational logic. While the subjectivist interpretation of quantum probability explains it as a reliable predictive tool for an agent in order to compute measurement outcomes, the objectivist interpretation understands quantum probability as providing reliable information of a real state of affairs. After discussing these different viewpoints we propose a particular objectivist interpretation grounded on the idea that the Born rule provides information about an intensive realm of reality. We then turn our attention to the way in which the subjectivist interpretation of probability is presently applied within both quantum computation and quantum computational logic. Taking as a standpoint our proposed intensive account of quantum probability we discuss the possibilities and advantages it might open for the modeling and development of both quantum computation and quantum computational logic
A new quantum approach to binary classification
No full textThis paper proposes a new quantum-like method for the binary classification applied to classical datasets. Inspired by the quantum Helstrom measurement, this innovative approach has enabled us to define a new classifier, called Helstrom Quantum Centroid (HQC). This binary classifier (inspired by the concept of distinguishability between quantum states) acts on density matrices—called density patterns—that are the quantum encoding of classical patterns of a dataset. In this paper we compare the performance of HQC with respect to twelve standard (linear and non-linear) classifiers over fourteen different datasets. The experimental results show that HQC outperforms the other classifiers when compared to the Balanced Accuracy and other statistical measures. Finally, we show that the performance of our classifier is positively correlated to the increase in the number of “quantum copies” of a pattern and the resulting tensor product thereof.</div
Representing continuous t-norms in quantum computation with mixed states
No full textA model of quantum computation is discussed in (Aharanov et al 1997 Proc.
13th Annual ACM Symp. on Theory of Computation, STOC pp 20–30) and
(Tarasov 2002 J. Phys. A: Math. Gen. 35 5207–35) in which quantum gates
are represented by quantum operations acting on mixed states. It allows one to
use a quantum computational model in which connectives of a four-valued logic
can be realized as quantum gates. In this model, we give a representation of
certain functions, known as t-norms (Menger 1942 Proc. Natl Acad. Sci. USA
37 57–60), that generalize the triangle inequality for the probability distributionvalued
metrics. As a consequence an interpretation of the standard operations
associated with the basic fuzzy logic (H ́ajek 1998 Metamathematics of Fuzzy
Logic (Trends in Logic vol 4) (Dordrecht: Kluwer)) is provided in the frame of
quantum computatio
On an explicit representation of the Łukasiewicz sum as a quantum operation
No full textThe aim of this work is to introduce a quantum operation able to implement, in an approximate way, the Łukasiewicz sum in the framework of quantum computation. Different techniques for improving this approximation are studied, and in particular, the use of quantum cloning machine is considered
Partial orbits of quantum gates and full three-particle entanglement
No full textWe introduce the notion of partial orbit for a given set of elementary quantum gates, and we study the action of different sets of gates on an initially three-particle disentangled state. We analyze the entanglement of the resulting quantum states by appealing to the violation of Svetlichny inequality. We find that the violation values are concentrated on specific regions. This constitutes evidence for the existence of a structure, which is quite different from that of a randomly generated (using the Haar measure) set of gates. In turn, this fact highlights the relevance of studying the physical properties of the partial orbits associated with different sets of elementary gates
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