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Hector Freytes

Publications and source records attributed to Hector Freytes.

At least 19 recordsLinked to original sources
arXiv2024

Distribution of Non-Locality On Quantum Random Circuits

In this work we explore how different types of resources are distributed among the states generated by quantum random circuits (QRC). We focus on multipartite non-locality, but we also analyze quantum correlations by appealing to different entanglement and non-classicality measures. We analyze the violation of Mermin and Svetlichny inequalities in order to get a glance at the distribution of nonlocality and genuine multipartite nonlocality. Next, we compare universal vs non-universal sets of gates, to gain insight into the problem of explaining quantum advantage. By comparing the results obtained with ideal (noiseless) vs noisy intermediate-scale quantum (NISQ) devices, we lay the basis of a certification protocol, which aims to quantify how robust is the resources distribution among the states that a given device can generate. We have implemented our non-locality-based benchmark on actual quantum processors with different architectures, in order to assess up to which point they are capable of reproducing the ideal results.

quant-ph↗
arXiv2021

Quantum State Discrimination for Supervised Classification

In this paper we investigate the connection between quantum information theory and machine learning. In particular, we show how quantum state discrimination can represent a useful tool to address the standard classification problem in machine learning. Previous studies have shown that the optimal quantum measurement theory developed in the context of quantum information theory and quantum communication can inspire a new binary classification algorithm that can achieve higher inference accuracy for various datasets. Here we propose a model for arbitrary multiclass classification inspired by quantum state discrimination, which is enabled by encoding the data in the space of linear operators on a Hilbert space. While our algorithm is quantum-inspired, it can be implemented on classical hardware, thereby permitting immediate applications.

quant-ph↗
arXiv2019

Quantum Probability: a reliable tool for an agent or a reliable source of reality?

In 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.

quant-ph↗
arXiv2019

Logical structures underlying quantum computing

In this work we advance a generalization of quantum computational logics capable of dealing with some important examples of quantum algorithms. We outline an algebraic axiomatization of these structures.

quant-ph↗
arXiv2017

The Cantor-Bernstein-Schroder theorem in algebra

The famous Cantor-Bernstein-Schroder theorem (CBS-theorem for short) of set theory was generalized by Sikorski and Tarski to σ-complete Boolean algebras. After this, numerous generalizations of the CBS-theorem, extending the Sikorski-Tarski version to different classes of algebras, have been established. Among these classes there are lattice ordered groups, orthomodular lattices, MV-algebras, residuated lattices, etc. This suggests to consider a common algebraic framework in which various versions of the CBS-theorem can be formulated. In this work we provide this algebraic framework establishing necessary and sufficient conditions for the validity of the theorem. We also show how this abstract framework includes the versions of the CBS-theorem already present in the literature as well as new versions of the theorem extended to other classes such as groups, modules, semigroups, rings, *-rings etc.

math.LO↗
arXiv2017

Pattern Recognition In Non-Kolmogorovian Structures

We present a generalization of the problem of pattern recognition to arbitrary probabilistic models. This version deals with the problem of recognizing an individual pattern among a family of different species or classes of objects which obey probabilistic laws which do not comply with Kolmogorov's axioms. We show that such a scenario accommodates many important examples, and in particular, we provide a rigorous definition of the classical and the quantum pattern recognition problems, respectively. Our framework allows for the introduction of non-trivial correlations (as entanglement or discord) between the different species involved, opening the door to a new way of harnessing these physical resources for solving pattern recognition problems. Finally, we present some examples and discuss the computational complexity of the quantum pattern recognition problem, showing that the most important quantum computation algorithms can be described as non-Kolmogorovian pattern recognition problems.

quant-ph↗
arXiv2016

Continuous Functions as Quantum Operations: a probabilistic approximation

In this note we propose a version of the classical Stone-Weierstrass theorem in the context of quantum operations, by introducing a particular class of quantum operations, dubbed polynomial quantum operations. This result permits to interpret from a probabilistic point of view, and up to a certain approximation, any continuous function from the real cube [0; 1]^n to the real interval [0; 1] as a quantum operation.

quant-ph↗
arXiv2014

Interpreting the modal Kochen-Specker theorem: possibility and many worlds in quantum mechanics

In 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 of 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 constraints to actualization, and thus, the relation between actual and possible realms.

quant-ph↗
arXiv2014

The square of opposition in orthomodular logic

In Aristotelian logic, categorical propositions are divided in Universal Affirmative, Universal Negative, Particular Affirmative and Particular Negative. Possible relations between two of the mentioned type of propositions are encoded in the square of opposition. The square expresses the essential properties of monadic first order quantification which, in an algebraic approach, may be represented taking into account monadic Boolean algebras. More precisely, quantifiers are considered as modal operators acting on a Boolean algebra and the square of opposition is represented by relations between certain terms of the language in which the algebraic structure is formulated. This representation is sometimes called the modal square of opposition. Several generalizations of the monadic first order logic can be obtained by changing the underlying Boolean structure by another one giving rise to new possible interpretations of the square.

quant-ph↗
arXiv2014

Quantum mechanics and the interpretation of the orthomodular square of opposition

In this paper we analyze and discuss the historical and philosophical development of the notion of logical possibility focusing on its specific meaning in classical and quantum mechanics. Taking into account the logical structure of quantum theory we continue our discussion regarding the Aristotelian Square of Opposition in orthomodular structures enriched with a monadic quantifier. Finally, we provide an interpretation of the Orthomodular Square of Opposition exposing the fact that classical possibility and quantum possibility behave formally in radically different manners.

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arXiv2014

Two-valued states on Baer $^*$-semigroups

In this paper we develop an algebraic framework that allows us to extend families of two-valued states on orthomodular lattices to Baer $^*$-semigroups. We apply this general approach to study the full class of two-valued states and the subclass of Jauch-Piron two-valued states on Baer $^*$-semigroups.

quant-ph↗
arXiv2012

Entities, Identity and the Formal Structure of Quantum Mechanics

The concept of individuality in quantum mechanics shows radical differences from the one used in classical physics. In particular, it is not possible to consider the fundamental particles described by quantum theory as individual distinguishable objects. In this paper we present arguments in favor of quantum non-individuality, which -in addition to those based on quantum statistics- relate to the Kochen-Specker theorem and the principle of superposition. Then, we analyze the possibility of referring to 'possible individuals' instead of 'actual individuals', and show that the Modal-Kochen-Specker theorem precludes this interpretational move.

quant-ph↗
arXiv2010

Quantum computational logic with mixed states

Using an algebraic framework we solve a problem posed in [5] and [7] about the axiomatizability of a quantum computational type logic related to fuzzy logic. A Hilbert-style calculus is developed obtaining an algebraic strong completeness theorem.

quant-ph↗
arXiv2008

Injectives in residuated algebras

Injectives in several classes of structures associated with logic are characterized. Among the classes considered are residuated lattices, MTL-algebras, IMTL-algebras, BL-algebras, NM-algebras and bounded hoops.

math.LO↗
arXiv2008

Pavelka-style completeness in expansions of Łukasiewicz logic

An algebraic setting for the validity of Pavelka style completeness for some natural expansions of Łukasiewicz logic by new connectives and rational constants is given. This algebraic approach is based on the fact that the standard MV-algebra on the real segment $[0, 1]$ is an injective MV-algebra. In particular the logics associated with MV-algebras with product and with divisible MV-algebras are considered.

math.LO↗