# Federico Hernán HolikNational Scientific and Technical Research Council | conicet · CCT La Plata

Federico Hernán Holik

PhD

www.quantumlogic.com.ar

## About

139

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Introduction

Additional affiliations

June 2014 - present

October 2013 - December 2013

June 2013 - October 2013

## Publications

Publications (139)

A general mathematical framework, based on countable partitions of Natural Numbers [1], is presented, that allows to provide a Semantics to propositional languages. It has the particularity of allowing both the valuations and the interpretation Sets for the connectives to discriminate complexity of the formulas. This allows different adequacy crite...

The problem of quantum state estimation is crucial in the development of quantum technologies. In particular, the use of symmetric quantum states is useful in many relevant applications. In this work, we analyze the task of reconstructing the density matrices of symmetric quantum states generated by a quantum processor. For this purpose, we take ad...

In this paper, we will try to establish the conditions of possibility of agency. We will present a notion of ‘freedom’, as opposed to the traditional concept of ‘free will’, based on a pluralistic and relational ontology that admits the existence of real possibilities. In contrast to the traditional view, we propose that ‘freedom’ is not a conditio...

In the present investigation diverse information quantifiers have been applied to the study of time-series of COVID-19. First, it has been analyzed how the smoothing of the curves affects the informative content of the series, using permutation and wavelet entropies for the series of new daily cases, by means of a sliding-windows’ method. Besides,...

This paper introduces the theory QST of quasets as a formal basis for the Nmatrices. The main aim is to construct a system of Nmatrices by substituting standard sets byquasets. Since QST is a conservative extension of ZFA (the Zermelo-Fraenkel set theory withAtoms), it is possible to obtain generalized Nmatrices (Q-Nmatrices). Since the original fo...

Mereology deals with the study of the relations between wholes and parts. In this work we will discuss different developments and open problems related to the formulation of a quantum mereology. In particular, we will discuss different advances in the development of formal systems aimed to describe the whole-parts relationship in the context of qua...

Link to publication:
https://royalsociety.org/blog/2023/07/identity-individuality-indistinguishability/

Quantum indistinguishability directly relates to the philosophical debate on the notions of identity and individuality. They are crucial for our understanding of multipartite quantum systems. Furthermore, the correct interpretation of this feature of quantum theory has implications that transcend fundamental science and philosophy, given that quant...

In this paper we discuss the notions of adequacy and truth functionality in quantum logic from the point of view of a non-deterministic semantics. We give a characterization of the degree of non-functionality which is compatible with the propositional
structure of quantum theory, showing that having truth-functional connectives, together with some...

By elaborating on the results presented in Lógica cuántica, Nmatrices y adecuación I, here we discuss the notions of adequacy and truth functionality in quantum logic from the
point of view of a non-deterministic semantics based on Nmatrices. We present a proof of the impossibility of providing a functional semantics for the quantum lattice. An ad...

The Jensen-Shannon divergence has been successfully applied as a segmentation tool for symbolic sequences, that is to separate the sequence into subsequences with the same symbolic content. In this work, we propose a method, based on the the Jensen-Shannon divergence, for segmentation of what we call \textit{quantum generated sequences}, which cons...

Resumen: Se presenta un marco matemático general, basado en particiones numerables de los números naturales [1], que permite brindar una semántica a lenguajes proposicionales. El mismo tiene la particularidad de permitir que tanto las valuaciones como los conjuntos de interpretación para los conectivos discriminen complejidad de las fórmulas. Esto...

In this work, we elaborate on a measure-theoretic approach to negative probabilities. We study a natural notion of contextuality measure and characterize its main properties. Then, we apply this measure to relevant examples of quantum physics. In particular, we study the role played by contextuality in quantum computing circuits.

We apply different information quantifiers to the study of COVID-19 time series. First, we analyze how the fact of smoothing the curves alters the informational content of the series, by applying the permutation and wavelet entropies to the series of daily new cases using a sliding-window method. In addition, to study how coupled the curves associa...

By elaborating on the results presented in Lógica cuántica, Nmatrices y adecuación I, here we discuss the notions of adequacy and truth functionality in quantum logic from the point of view of a non-deterministic semantics based on Nmatrices. We present a proof of the impossibility of providing a functional semantics for the quantum lattice. An adv...

Since the appearance in China of the first cases, the entire world has been deeply affected by the flagellum of the Coronavirus Disease (COVID-19) pandemic. There have been many mathematical approaches trying to characterize the data collected about this serious issue. One of the most important aspects for attacking a problem is knowing what inform...

In this review, we present a rigorous construction of an algebraic method for quantum unstable states, also called Gamow states. A traditional picture associates these states to vectors states called Gamow vectors. However, this has some difficulties. In particular, there is no consistent definition of mean values of observables on Gamow vectors. I...

In this work, we show how to parameterize a density matrix that has an arbitrary symmetry, knowing the generators of the Lie algebra (if the symmetry group is a connected Lie group) or the generators of its underlying group (in case it is finite). This allows to pose MaxEnt and MaxLik estimation techniques as convex optimization problems with a sub...

En este trabajo discutimos las nociones de adecuación y veritativo-funcionalidad en la lógica cuántica desde el punto de vista de una semántica no determinista. Damos una caracterización del grado de no-funcionalidad compatible con la estructura proposicional de la teoría cuántica, presentando una prueba de la imposibilidad de asignar una semántica...

Se introduce la teoría de quaset QST en la base formal de las Nmatrices. El objetivo es construir un sistema Nmatricial reemplazando en su formulación todos los conjuntos estándar por quasets. De esta manera, debido a que QST es una extensión conservativa de ZFA (ZF con átomos), pueden obtenerse Nmatrices generalizadas (Q-Nmatrices). Se presentan d...

In this work, we focus on the philosophical aspects and technical challenges that underlie the axiomatization of the non-Kolmogorovian probability framework, in connection with the problem of quantum contextuality. This fundamental feature of quantum theory has received a lot of attention recently, given that it might be connected to the speed-up o...

In previous works, an ontology of properties for quantum mechanics has been pro�posed, according to which quantum systems are bundles of properties with no principle of individuality. The aim of the present article is to show that, since quasi-set theory is particularly suited for dealing with aggregates of items that do not belong to the tradition...

In previous works, an ontology of properties for quantum mechanics has been proposed, according to which quantum systems are bundles of properties with no principle of individuality. The aim of the present article is to show that, since quasi-set theory is particularly suited for dealing with aggregates of items that do not belong to the traditiona...

When an informationally complete measurement is not available, the reconstruction of the density operator that describes the state of a quantum system can be obtained, in a reliable way, by adopting the maximum entropy principle (MaxEnt principle), as an additional criterion, to achieve the least biased estimation. In this paper, we study the perfo...

In this work we study the reduced density matrices of sublattices of fermionic, bosonic and spin lattice models. Firstly, we consider fermionic and bosonic lattice models, and we show that the reduced density matrix associated with a sublattice coincides with the state obtained by applying the maximum entropy principle under suitably chosen constra...

In this paper, we discuss content and context for quantum properties. We give some examples of why quantum properties are problematic: they depend on the context in a non-trivial way. We then connect this difficulty with properties to the indistinguishability of elementary particles. We argue that one could be in trouble in applying the classical t...

We 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 concentr...

In previous works, an ontology of properties for quantum mechanics has been proposed, according to which quantum systems are bundles of properties with no principle of individuality. The aim of the present article is to show that, since quasi-set theory is particularly suited for treating aggregates of items that do not belong to the traditional ca...

When an informationally complete measurement is not available, the reconstruction of the density operator that describes the state of a quantum system can be accomplish, in a reliable way,
by adopting the maximum entropy principle (MaxEnt principle), as an additional criterion, to obtain the least biased estimation. In this paper, we study the perf...

Since the appearance in China of the first cases, the world has been affected by the flagellum of the Coronavirus Disease (COVID-19) pandemic. There have been many mathematical approaches trying to characterize the data collected about this serious issue. One of the most important aspects for attacking a problem is knowing what information is reall...

In this paper we investigate measures over bounded lattices, extending and giving a unifying treatment to previous works. In particular, we prove that the measures of an arbitrary bounded lattice can be represented as measures over a suitably chosen Boolean lattice. Using techniques
from algebraic geometry, we also prove that given a bounded lattic...

In this paper, we discuss content and context for quantum properties. We give some examples of why quantum properties are problematic: they depend on the context in a non-trivial way. We then connect this difficulty with properties to the indistinguishability of elementary particles. We argue that one could be in trouble in applying the classical t...

You can watch the Conference talk in the following link:
https://www.youtube.com/watch?v=e6OBrSOtcKM

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...

The Kochen-Specker theorem is one of the fundamental no-go theorems in quantum theory. It has far-reaching consequences for all attempts trying to give an interpretation of the quantum formalism. In this work, we examine the hypotheses that, at the ontological level, lead to the KochenSpecker contradiction. We emphasize the role of the assumptions...

We discuss the mathematical structures that underlie quantum probabilities. More specifically, we explore possible connections between logic, geometry and probability theory. We propose an interpretation that generalizes the method developed by R. T. Cox to the quantum logical approach to physical theories. We stress the relevance of developing a g...

We discuss the mathematical structures that underlie quantum probabilities. More specifically, we explore possible connections between logic, geometry and probability theory. We propose an interpretation that generalizes the method developed by R. T. Cox to the quantum logical approach to physical theories. We stress the relevance of developing a g...

The Kochen-Specker theorem is one of the fundamental no-go theorems in quantum theory. It has far-reaching consequences for all attempts trying to give an interpretation of the quantum formalism. In this work, we examine the hypotheses that, at the ontological level, lead to the KochenSpecker contradiction. We emphasize the role of the assumptions...

In previous works, an ontology of properties for quantum mechanics has been proposed, according to which quantum systems are bundles of properties with no principle of individuality. The aim of the present article is to show that, since quasi-set theory is particularly suited for treating aggregates of items that do not belong to the traditional ca...

We discuss a reconstruction of standard quantum mechanics assuming indistinguishability right from the start, by appealing to quasi-set theory. After recalling the fundamental aspects of the construction and introducing some improvements in the original formulation, we extract some conclusions for the interpretation of quantum theory.

Gamow vectors have been developed in order to give a mathematical description for quantum decay phenomena. Mainly, they have been applied to radioactive phenomena, scattering and to some decoherence models. They play a crucial role in the description of quantum irreversible processes, and in the formulation of time asymmetry in quantum mechanics. I...

Gamow vectors have been developed in order to give a mathematical description for quantum decay phenomena. Mainly, they have been applied to radioactive phenomena,
scattering and to some decoherence models. They play a crucial role in the description of quantum irreversible processes and in the formulation of time asymmetry in quantum mechanics. In...

In this paper, we examined the connection between quantum systems’ indistinguishability and signed (or negative) probabilities. We do so by first introducing a measure-theoretic definition of signed probabilities inspired by research in quantum contextuality. We then argue that ontological indistinguishability leads to the no-signaling condition an...

In this paper, we examined the connection between quantum systems' indistinguishability and signed (or negative) probabilities. We do so by first introducing a measure-theoretic definition of signed probabilities inspired by research in quantum contextuality. We then argue that ontological indistinguishability leads to the no-signaling condition an...

A fundamental aspect of the quantum-to-classical limit is the transition from a non-commutative algebra of observables to commutative one. However, this transition is not possible if we only consider unitary evolutions. One way to describe this transition is to consider the Gamow vectors, which introduce exponential decays in the evolution. In this...

Given a probability vector x with its components sorted in non-increasing order, we consider the closed ball Bp (x) with p 1 formed by the probability vectors whose p-norm distance to the center x is less than or equal to a radius . Here, we provide an order-Theoretic characterization of these balls by using the majorization partial order. Unlike t...

In this work, we discuss the failure of the principle of truth functionality in the quantum formalism. By exploiting this failure, we import the formalism of N-matrix theory and non-deterministic semantics to the foundations of quantum mechanics. This is done by describing quantum states as particular valuations associated with infinite non-determi...

Given a probability vector $x$ with its components sorted in non-increasing order, we consider the closed ball ${\mathcal{B}}^p_\epsilon(x)$ with $p \geq 1$ formed by the probability vectors whose $\ell^p$-norm distance to the center $x$ is less than or equal to a radius $\epsilon$. Here, we provide an order-theoretic characterization of these ball...

We discuss a reconstruction of standard quantum mechanics assuming indistinguishability right from the start, by appealing to quasi-set theory. After recalling the fundamental aspects of the construction and introducing some improvements in the original formulation, we extract some conclusions for the interpretation of quantum theory.

In this work, we discuss a formal way of dealing with the properties of contextual systems. Our approach is to assume that properties describing the same physical quantity, but belonging to different measurement contexts, are indistinguishable in a strong sense. To construct the formal theoretical structure, we develop a description using quasi-set...

In this paper, we deal with the situation in which the unknown state of a quantum system has to be estimated under the assumption that it is prepared obeying a known set of symmetries. We present a system of equations and an explicit solution for the problem of determining the MaxEnt state satisfying these constraints. Our approach can be applied t...

We address the problem of finding the optimal common resource for an arbitrary family of target states in quantum resource theories based on majorization, that is, theories whose conversion law between resources is determined by a majorization relationship, such as it happens with entanglement, coherence or purity. We provide a conclusive answer to...

In this paper, we deal with the situation in which the unknown state of a quantum system has to be estimated under the assumption that it is prepared obeying a known set of symmetries. We present a system of equations and an explicit solution for the problem of determining the MaxEnt state satisfying these constraints. Our approach can be applied t...

In this work we discuss a formal way of dealing with properties of con-textual systems. Our approach is to assume that properties describing the same physical quantity, but belonging to different measurement contexts, are indistinguishable in a strong sense. To construct the formal theoretical structure, we develop a description using quasi-set the...

A fundamental aspect of the quantum-to-classical limit is the transition from a non-commutative algebra of observables to commutative one. However, this transition is not possible if we only consider unitary evolutions. One way to describe this transition is to consider the Gamow vectors, which introduce exponential decays in the evolution. In this...

In this work we provide a connection between the Kochen-Specker theorem in quantum mechanics and the failure of the principle truth functionality in logic. By exploiting this connection, we import the formalism of N-matrix theory and non-deterministic semantics to the foundations of quantum mechanics. This is done by describing quantum states as pa...

The 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.

In order to characterize quantum states within the context of information geometry, we propose a generalization of the Gaussian model, which we called the Hermite–Gaussian model. We obtain the Fisher–Rao metric and the scalar curvature for this model, and we show its relation with the one-dimensional quantum harmonic oscillator. Using this model we...

The VII Conference on Quantum Foundations: 90 years of uncertainty was held during November29th to December 1st, in 2017, at the Facultad de Matemática, Astronomía, Física y Computación,Córdoba, Argentina[...]

We address the problem of finding the optimal common resource for an arbitrary family of target states in quantum resource theories based on majorization, that is, theories whose conversion law between resources is determined by a majorization relationship, such as it happens with entanglement, coherence or purity. We provide a conclusive answer to...

We address the problem of finding the optimal common resource for an arbitrary family of target states in quantum resource theories based on majorization, that is, theories whose conversion law between resources is determined by a majorization relationship, such as it happens with entanglement, coherence or purity. We provide a conclusive answer to...

We present a characterization of states in generalized probabilistic models by appealing to a non-commutative version of geometric probability theory based on algebraic geometry techniques. Our theoretical framework allows for incorporation of invariant states in a natural way.

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.

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.

In order to characterize quantum states within the context of information geometry, we propose a generalization of the Gaussian model, which we called the Hermite-Gaussian model. We obtain the Fisher-Rao metric and the scalar curvature for this model, and we show its relation with the one-dimensional quantum harmonic oscillator. Moreover, using thi...

In order to characterize quantum states within the context of information geometry, we propose a generalization of the Gaussian model, which we called the Hermite-Gaussian model. We obtain the Fisher-Rao metric and the scalar curvature for this model, and we show its relation with the one-dimensional quantum harmonic oscillator. Moreover, using thi...

We study a version of the generalized (h, ϕ)-entropies, introduced by Salicrú et al. [M. Salicrú et al., Commun. Stat. Theory Method. 22, 2015 (1993)], for a wide family of probabilistic models that includes quantum and classical statistical theories as particular cases. We extend previous works by exploring how to define (h, ϕ)-entropies in infini...

We present a system of equations and an explicit solution for the problem of determining the MaxEnt state of a quantum system satisfying symmetry constraints.

We introduce a dynamical evolution operator for dealing with unstable physical process, such as scattering resonances, photon emission, decoherence and particle decay. With that aim, we use the formalism of rigged Hilbert space and represent the time evolution of quantum observables in the Heisenberg picture, in such a way that time evolution is no...

In this work we discuss logical structures related to indistinguishable (or similar) particles. Most of the framework used to develop these structures was presented in previous works. We use these structures and constructions to discuss possible ontologies for identical particles. In other words, we use these structures in order to characterize the...

We introduce a dynamical evolution operator for dealing with unstable physical process, such as scattering resonances, photon emission, decoherence and particle decay. With that aim, we use the formalism of rigged Hilbert space and represent the time evolution of quantum observables in the Heisenberg picture, in such a way that time evolution is no...

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...

We study a version of the generalized (h, φ)-entropies, introduced by Salicrú et al, for a wide family of probabilistic models that includes quantum and classical statistical theories as particular cases. We extend previous works by exploring how to define (h, φ)-entropies in infinite dimensional models.

We study a version of the generalized (h, {\phi})-entropies, introduced by Salicr\'u et al, for a wide family of probabilistic models that includes quantum and classical statistical theories as particular cases. We extend previous works by exploring how to define (h, {\phi})-entropies in infinite dimensional models.

The analysis of the classical limit of quantum mechanics usually focuses on the state of the system. The general idea is to explain the disappearance of the interference terms of quantum states appealing to the decoherence process induced by the environment. However, in these approaches it is not explained how the structure of quantum properties be...

Based on the problem of quantum data compression in a lossless way, we present here an operational interpretation for the family of quantum Rényi entropies. In order to do this, we appeal to a very general quantum encoding scheme that satisfies a quantum version of the Kraft-McMillan inequality. Then, in the standard situation, where one is intende...

It is well known that in quantum mechanics we cannot always define consistently properties that are context independent. Many approaches exist to describe contextual properties, such as Contextuality by Default (CbD), sheaf theory, topos theory, and non-standard or signed probabilities. In this paper we propose a treatment of contextual properties...

Combining physics and philosophy, this is a uniquely interdisciplinary examination of quantum information science which provides an up-to-date examination of developments in this field. The authors provide coherent definitions and theories of information, taking clearly defined approaches to considering information in connection with quantum mechan...