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Federico Holik

Publications and source records attributed to Federico Holik.

At least 19 recordsLinked to original sources
arXiv2026

Quantum skyrmions in the antiferromagnetic triangular lattice

Magnetic skyrmions are topological quasiparticles potentially useful for memory and computing devices. Antiferromagnetic (AF) skyrmions present no transverse deflection, making them suitable candidates for data storage applications. After the discovery of skyrmions with length scales comparable to the lattice constant, several works presented quantum analogues of classical ferromagnetic skyrmions in spin systems. However, studies about quantum analogues of AF skyrmions are still lacking. Here, we explore the phases of the AF quantum spin-1/2 Heisenberg model with Dzyaloshinskii-Moriya interactions on the triangular lattice using the density matrix renormalization group (DMRG) algorithm. We study the magnetization profile, spin structure factor and quantum entanglement of the resulting ground states to characterize the corresponding phases and signal the emergence of quantum AF skyrmions. Our results support that three-sublattice quantum antiferromagnetic skyrmion textures are stabilized in a wide range of magnetic fields.

cond-mat.str-el↗
arXiv2024

Group-invariant estimation of symmetric states generated by noisy quantum computers

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 advantage of an estimation technique that results to be equivalent to the quantum Maximum Entropy (MaxEnt) estimation, and which was recently adapted to quantum states with arbitrary symmetries. The smart use of prior knowledge of the quantum state symmetries allows for a reduction in both, the number of measurements that need to be made on the system, and the size of the computational problem to store and process the data, resulting in a better overall performance of the estimator as well. After performing numerical simulations, we implement some examples of symmetric states in IonQ quantum processors, and estimate them using the proposed technique. The results are in a good agreement with numerical simulations, showing that the proposed method is a good estimator that allows to save both, experimental and computational resources.

quant-ph↗
arXiv2023

Segmentation of quantum generated sequences by using the Jensen-Shannon divergence

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 consist in symbolic sequences generated from measuring a quantum system. For one-qubit and two-qubit systems, we show that the proposed method is adequate for segmentation.

quant-ph↗
arXiv2023

Measure-theoretic approach to negative probabilities

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.

quant-ph↗
arXiv2022

Parameterizing density operators with arbitrary symmetries to gain advantage in quantum state estimation

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 substantial reduction in the number of parameters of the function involved. This implies that, apart from a computational advantage due to the fact that the optimization is performed in a reduced space, the amount of experimental data needed for a good estimation of the density matrix can be reduced as well. In addition, we run numerical experiments and apply these parameterizations to quantum state estimation of states with different symmetries.

quant-ph↗
arXiv2022

Performance of the quantum MaxEnt estimation in the presence of physical symmetries

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 performance of the MaxEnt method for quantum state estimation when there is prior information about symmetries of the unknown state. We explicitly describe how to work with this method in the most general case, and present an algorithm that allows to improve the estimation of quantum states with arbitrary symmetries. Furthermore, we implement this algorithm to carry out numerical simulations estimating the density matrix of several three-qubit states of particular interest for quantum information tasks. We observed that, for most states, our approach allows to considerably reduce the number of independent measurements needed to obtain a sufficiently high fidelity in the reconstruction of the density matrix. Moreover, we analyze the performance of the method in realistic scenarios, showing that it is robust even when considering the effect of finite statistics, and under the presence of typical experimental noise.

quant-ph↗
arXiv2021

Quantum identity, content, and context: from classical to non-classical logic

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 theory of identity to the quantum domain if we take indiscernibility as a core and fundamental concept. Thus, in considering indistinguishability as such a fundamental notion, it implies, if taken earnestly, that one should not apply standard logic to quantum objects. Consequently, we end with a discussion about novel aspects this new mathematics brings and how it relates to some issues associated with the quantum world's ontology and the classical limit. We emphasize that, despite several different ways of questioning classical logic in the quantum domain, our approach is distinct. It involves one of the core concepts of classical logic, namely, identity. So, we are in a different paradigm from standard quantum logics.

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↗
arXiv2021

On the assumptions underlying KS-like contradictions

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 about identity and distinguishability of quantum objects in the argument.

quant-ph↗
arXiv2020

Gamow vectors formalism applied to the Loschmidt echo

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 this paper, we use this formalism to describe a well-known phenomenon of irreversibility: the Loschmidt echo. The standard approach considers that the irreversibility of this phenomenon is the result of an additional term in the backward Hamiltonian. Here, we use the non-Hermitian formalism, where the time evolution is non-unitary. Additionally, we compare the characteristic decay times of this phenomenon with the decoherence ones. We conclude that the Loschmidt echo and the decoherence can be considered as two aspects of the same phenomenon, and that there is a mathematical relationship between their corresponding characteristic times.

quant-ph↗
arXiv2020

Indistinguishability and Negative Probabilities

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 and negative probabilities.

quant-ph↗
arXiv2020

Non-deterministic semantics for quantum states

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 to infinite non-deterministic truth tables. This allows us to introduce a natural interpretation of quantum states in terms of a non-deterministic semantics. We also provide a similar construction for arbitrary probabilistic theories based in orthomodular lattices, allowing to study post-quantum models using logical techniques.

quant-ph↗
arXiv2020

Extremal elements of a sublattice of the majorization lattice and approximate majorization

Given a probability vector $x$ with its components sorted in non-increasing order, we consider the closed ball ${\mathcal{B}}^p_ε(x)$ 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 $ε$. Here, we provide an order-theoretic characterization of these balls by using the majorization partial order. Unlike the case $p=1$ previously discussed in the literature, we find that the extremal probability vectors, in general, do not exist for the closed balls ${\mathcal{B}}^p_ε(x)$ with $1<p<\infty$. On the other hand, we show that ${\mathcal{B}}^\infty_ε(x)$ is a complete sublattice of the majorization lattice. As a consequence, this ball has also extremal elements. In addition, we give an explicit characterization of those extremal elements in terms of the radius and the center of the ball. This allows us to introduce some notions of approximate majorization and discuss its relation with previous results of approximate majorization given in terms of the $\ell^1$-norm. Finally, we apply our results to the problem of approximate conversion of resources within the framework of quantum resource theory of nonuniformity.

quant-ph↗
arXiv2019

Indistinguishability and the origins of contextuality in physics

In this work we discuss a formal way of dealing with 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 theory, which is a set-theoretical framework built to describe collections of elements that violate Leibnitz's principle of identity of indiscernibles. This allows us to consider a new ontology in order to study properties of quantum systems.

quant-ph↗
arXiv2019

Evolution of quantum observables: from non-commutativity to commutativity

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 paper, we give two mathematical models in which this transition happens in the infite time limit. In the first one, we consider operators acting on the space of the Gamow vectors, which represent quantum resonances. In the second one, we use an algebraic formalism from scattering theory. We construct a non-commuting algebra which commutes in the infinite time limit.

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↗
arXiv2018

Hermite-Gaussian model for quantum states

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 this model we characterize some failies of states of the quantum harmonic oscillator. We find that for the eigenstates of the Hamiltonian, mixtures of eigenstates and even or odd superpositions of eienstates the associated Fisher-Rao metrics are diagonal.

math-ph↗