arXiv subjects

P. W. Lamberti

Publications and source records attributed to P. W. Lamberti.

At least 19 recordsLinked to original sources

arXiv2019

Behavior of quantum correlations under nondissipative decoherence by means of the correlation matrix

In this paper we use the Fano representation of two-qubit states from which we can identify a correlation matrix containing the information about the classical and quantum correlations present in the bipartite quantum state. To illustrate the use of this matrix, we analyze the behavior of the correlations under non-dissipative decoherence in two-qubit states with maximally mixed marginals. From the behavior of the elements of the correlation matrix before and after making measurements on one of the subsystems, we identify the classical and quantum correlations present in the Bell-diagonal states. In addition, we use the correlation matrix to study the phenomenon known as freezing of quantum discord. We find that under some initial conditions where freezing of quantum discord takes place, quantum correlation instead may remain not constant. In order to further explore into these results we also compute a non-commutativity measure of quantum correlations to analyze the behavior of quantum correlations under non-dissipative decoherence. We conclude from our study that freezing of quantum discord may not always be identified as equivalent to the freezing of the actual quantum correlations.

quant-ph↗

arXiv2019

Generalized approach to quantify correlations in bipartite quantum systems

In this work we developed a general approach to the problem of detecting and quantifying different kind of correlations in bipartite quantum systems. Our method is based on the use of distances between quantum states and processes. We rely upon the premise that total correlations can be separated into classical and quantum contributions due to their different nature. In addition, according to recently discussed criteria, we determined the requirements to be satisfied by distances in order to generate correlation measures physically well behaved. The proposed measures allow us to quantify quantum, classical and total correlations.

quant-ph↗

arXiv2018

Generalized entropies in quantum and classical statistical theories

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.

quant-ph↗

arXiv2017

Problem of quantifying quantum correlations with non-commutative discord

In this work we analyze a non-commutativity measure of quantum correlations recently proposed by Y. Guo [Sci. Rep. 6, 25241 (2016)]. By recourse to a systematic survey of a two-qubit system, we detected an undesirable behavior of such a measure related to its representation-dependence. In the case of pure states, this dependence manifests as a non-satisfactory entanglement measure whenever a representation other than the Schmidt's is used. In order to avoid this dependence on the basis, we argue that a minimization procedure over the set of all possible representations of the quantum state is required. In the case of pure states, this minimization can be analytically performed and the optimal basis turns out to be that of Schmidt's. In addition, the resulting measure inherits the main properties of Guo's measure and, unlike the latter, it reduces to a legitimate entanglement measure in the case of pure states. Some examples involving general mixed states are also analyzed considering such a optimization. The results show that, in most cases of interest, the use of Guo's measure can result in a overestimation of quantum correlations. However, since Guo's measure has the advantage of being easily computable, it might be used as a qualitative estimator of the presence of quantum correlations.

quant-ph↗

arXiv2017

Detecting dynamical changes in time series by using the Jensen Shannon Divergence

Most of the time series in nature are a mixture of signals with deterministic and random dynamics. Thus the distinction between these two characteristics becomes important. Distinguishing between chaotic and aleatory signals is difficult because they have a common wide-band power spectrum, a delta-like autocorrelation function, and share other features as well. In general signals are presented as continuous records and require to be discretized for being analyzed. In this work we present different schemes for discretizing and for detection of dynamical changes in time series. One of the main motivations is to detect transition from chaotic regime to random regime. The tools used are originated in Information Theory. The schemes proposed are applied to simulated and real life signals, showing in all cases a high proficiency for detecting changes in the dynamics of the associated time series.

physics.data-an↗

arXiv2016

A family of generalized quantum entropies: definition and properties

We present a quantum version of the generalized $(h,ϕ)$-entropies, introduced by Salicrú \textit{et al.} for the study of classical probability distributions. We establish their basic properties, and show that already known quantum entropies such as von Neumann, and quantum versions of Rényi, Tsallis, and unified entropies, constitute particular classes of the present general quantum Salicrú form. We exhibit that majorization plays a key role in explaining most of their common features. We give a characterization of the quantum $(h,ϕ)$-entropies under the action of quantum operations, and study their properties for composite systems. We apply these generalized entropies to the problem of detection of quantum entanglement, and introduce a discussion on possible generalized conditional entropies as well.

quant-ph↗

arXiv2016

Unified entropic measures of quantum correlations induced by local measurements

We introduce quantum correlations measures based on the minimal change in unified entropies induced by local rank-one projective measurements, divided by a factor that depends on the generalized purity of the system in the case of non-additive entropies. In this way, we overcome the issue of the artificial increasing of the value of quantum correlations measures based on non-additive entropies when an uncorrelated ancilla is appended to the system without changing the computability of our entropic correlations measures with respect to the previous ones. Moreover, we recover as limiting cases the quantum correlations measures based on von Neumann and Rényi entropies (i.e., additive entropies), for which the adjustment factor becomes trivial. In addition, we distinguish between total and semiquantum correlations and obtain some relations between them. Finally, we obtain analytical expressions of the entropic correlations measures for typical quantum bipartite systems.

quant-ph↗

arXiv2014

Geometric approach to extend Landau-Pollak uncertainty relations for positive operator-valued measures

We provide a twofold extension of Landau--Pollak uncertainty relations for mixed quantum states and for positive operator-valued measures, by recourse to geometric considerations. The generalization is based on metrics between pure states, having the form of a function of the square of the inner product between the states. The triangle inequality satisfied by such metrics plays a crucial role in our derivation. The usual Landau--Pollak inequality is thus a particular case (derived from Wootters metric) of the family of inequalities obtained, and, moreover, we show that it is the most restrictive relation within the family.

quant-ph↗

arXiv2014

Mixing Bandt-Pompe and Lempel-Ziv approaches: another way to analyze the complexity of continuous-states sequences

In this paper, we propose to mix the approach underlying Bandt-Pompe permutation entropy with Lempel-Ziv complexity, to design what we call Lempel-Ziv permutation complexity. The principle consists of two steps: (i) transformation of a continuous-state series that is intrinsically multivariate or arises from embedding into a sequence of permutation vectors, where the components are the positions of the components of the initial vector when re-arranged; (ii) performing the Lempel-Ziv complexity for this series of `symbols', as part of a discrete finite-size alphabet. On the one hand, the permutation entropy of Bandt-Pompe aims at the study of the entropy of such a sequence; i.e., the entropy of patterns in a sequence (e.g., local increases or decreases). On the other hand, the Lempel-Ziv complexity of a discrete-state sequence aims at the study of the temporal organization of the symbols (i.e., the rate of compressibility of the sequence). Thus, the Lempel-Ziv permutation complexity aims to take advantage of both of these methods. The potential from such a combined approach - of a permutation procedure and a complexity analysis - is evaluated through the illustration of some simulated data and some real data. In both cases, we compare the individual approaches and the combined approach.

physics.data-an↗

arXiv2013

A geometric formulation of uncertainty principle

A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a projector associated with an observable, and interpret it as the probability of obtaining the outcome corresponding to that projector. We make use of fidelity-based metrics such as angle, Bures and root-infidelity ones, to propose a measure of uncertainty. The triangle inequality allows us to derive a family of uncertainty relations. In the case of the angle metric, we re-obtain the Landau--Pollak inequality for pure states and show, in a natural way, how to extend it to the case of mixed states in arbitrary dimension. In addition, we derive and compare novel uncertainty relations when using other known fidelity-based metrics.

quant-ph↗

arXiv2013

Effect of microtubule-associated protein tau in dynamics of single-headed motor proteins KIF1A

Intracellular transport based on molecular motors and its regulation are crucial to the functioning of cells. Filamentary tracks of the cells are abundantly decorated with non-motile microtubule-associated proteins, such as tau. Motivated by experiments on kinesin-tau interactions [Dixit et al. Science 319, 1086 (2008)] we developed a stochastic model of interacting single-headed motor proteins KIF1A that also takes into account the interactions between motor proteins and tau molecules. Our model reproduce experimental observations and predicts significant effects of tau on bound time and run length which suggest an important role of tau in regulation of kinesin-based transport.

physics.bio-ph↗

arXiv2011

An H-theorem for the Brownian motion on the hyperbolic plane

We prove an $H-$theorem for the Brownian motion on the hyperbolic plane with a drift, as studied by Comtet and Monthus; the entropy used here is not the Boltzmann entropy but the Rényi entropy, the parameter of which being related in a simple way to the value of the drift.

cond-mat.stat-mech↗

arXiv2009

Natural Metric for Quantum Information Theory

We study in detail a very natural metric for quantum states. This new proposal has two basic ingredients: entropy and purification. The metric for two mixed states is defined as the square root of the entropy of the average of representative purifications of those states. Some basic properties are analyzed and its relation with other distances is investigated. As an illustrative application, the proposed metric is evaluated for 1-qubit mixed states.

quant-ph↗

arXiv2009

Cariñena polynomials are Jacobi polynomials

We show that the Cariñena orthogonal polynomials are Jacobi polynomials; moreover, there exists a natural bijection between the negative and the positive curvature cases. These results hold only in the two dimensional case.

math.CA↗

arXiv2008

On the metric character of the quantum Jensen-Shannon divergence

In a recent paper, the generalization of the Jensen Shannon divergence (JSD) in the context of quantum theory has been studied (Phys. Rev. A 72, 052310 (2005)). This distance between quantum states has shown to verify several of the properties required for a good distinguishability measure. Here we investigate the metric character of this distance. More precisely we show, formally for pure states and by means of simulations for mixed states, that its square root verifies the triangle inequality.

quant-ph↗

arXiv2008

Jensen Shannon divergence as a measure of the degree of entanglement

The notion of distance in Hilbert space is relevant in many scenarios. In particular, distances between quantum states play a central role in quantum information theory. An appropriate measure of distance is the quantum Jensen Shannon divergence (QJSD) between quantum states. Here we study this distance as a geometrical measure of entanglement and apply it to different families of states.

quant-ph↗

arXiv2005

Jensen-Shannon divergence as a measure of distinguishability between mixed quantum states

We discuss an alternative to relative entropy as a measure of distance between mixed quantum states. The proposed quantity is an extension to the realm of quantum theory of the Jensen-Shannon divergence (JSD) between probability distributions. The JSD has several interesting properties. It arises in information theory and, unlike the Kullback-Leibler divergence, it is symmetric, always well defined and bounded. We show that the quantum JSD (QJSD) shares with the relative entropy most of the physically relevant properties, in particular those required for a "good" quantum distinguishability measure. We relate it to other known quantum distances and we suggest possible applications in the field of the quantum information theory.

quant-ph↗

arXiv2004

Wootters' distance revisited: a new distinguishability criterium

The notion of distinguishability between quantum states has shown to be fundamental in the frame of quantum information theory. In this paper we present a new distinguishability criterium by using a information theoretic quantity: the Jensen-Shannon divergence (JSD). This quantity has several interesting properties, both from a conceptual and a formal point of view. Previous to define this distinguishability criterium, we review some of the most frequently used distances defined over quantum mechanics' Hilbert space. In this point our main claim is that the JSD can be taken as a unifying distance between quantum states.

quant-ph↗