arXiv subjects

Pedro W. Lamberti

Publications and source records attributed to Pedro W. Lamberti.

11 recordsLinked to original sources

arXiv2026

Quantum imaginary time evolution and UD-MIS problem

In this work we apply a procedure based on the quantum imaginary time evolution method to solve the unit-disk maximum independent set problem. Numerical simulations were performed for instances of 6, 8 and 10-qubits graphs. We have found that the failure probability of the procedure is relatively small and rapidly decreases with the number of shots. In addition, a theoretical upper bound for the failure probability of the procedure was obtained.

quant-ph↗

arXiv2023

Rényi-Holevo inequality from $α$-$z$-Rényi relative entropies

We investigate bounds in the transmission of classical information through quantum systems. Our focus lies in the generalized Holevo theorem, which provides a single-letter Holevo-like inequality from arbitrary quantum distance measures. Through the introduction of the $α$-$z$-Rényi relative entropies, which comprise known relevant quantities such as the Rényi relative entropy and the sandwiched Rényi relative entropy, we establish the Holevo-Rényi inequality. This result leads to a quantum bound for the $α$-mutual information, suggesting new insights into communication channel performance and the fundamental limits for reliability functions in memoryless multi-letter communication channels.

quant-ph↗

arXiv2023

Transmission distance in the space of quantum channels

We analyze two ways to obtain distinguishability measures between quantum maps by employing the square root of the quantum Jensen-Shannon divergence, which forms a true distance in the space of density operators. The arising measures are the transmission distance between quantum channels and the entropic channel divergence. We investigate their mathematical properties and discuss their physical meaning. Additionally, we establish a chain rule for the entropic channel divergence, which implies the amortization collapse, a relevant result with potential applications in the field of discrimination of quantum channels and converse bounds. Finally, we analyze the distinguishability between two given Pauli channels and study exemplary Hamiltonian dynamics under decoherence.

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↗

arXiv2022

Rao-Burbea centroids applied to the statistical characterisation of time series and images through ordinal patterns

Divergences or similarity measures between probability distributions have become a very useful tool for studying different aspects of statistical objects such as time series, networks and images. Notably not every divergence provides identical results when applied to the same problem. Therefore it is convenient to have the widest possible set of divergences to be applied to the problems under study. Besides this choice an essential step in the analysis of every statistical object is the mapping of each one of their representing values into an alphabet of symbols conveniently chosen. In this work we attack both problems, that is, the choice of a family of divergences and the way to do the map into a symbolic sequence. For advancing in the first task we work with the family of divergences known as the Burbea-Rao centroids (BRC) and for the second one we proceed by mapping the original object into a symbolic sequence through the use of ordinal patterns. Finally we apply our proposals to analyse simulated and real time series and to real textured images. The main conclusion of our work is that the best BRC, at least in the studied cases, is the Jensen Shannon divergence, besides the fact that it verifies some interesting formal properties.

cs.IT↗

arXiv2019

Generalized Holevo theorem and distinguishability notions

We present a generalization of the Holevo theorem by means of distances used in the definition of distinguishability of states, showing that each one leads to an alternative Holevo theorem. This result involves two quantities: the generalized Holevo information and the generalized accessible information. Additionally, we apply the new inequalities to qubits ensembles showing that for the Kolmogorov notion of distinguishability (for the case of an ensemble of two qubits) the generalized quantities are equal. On the other hand, by using a known example, we show that the Bhattacharyya notion captures not only the non-commutativity of the ensemble but also its purity.

quant-ph↗

arXiv2017

Monoparametric family of metrics derived from classical Jensen-Shannon divergence

Jensen-Shannon divergence is a well known multi-purpose measure of dissimilarity between probability distributions. It has been proven that the square root of this quantity is a true metric in the sense that, in addition to the basic properties of a distance, it also satisfies the triangle inequality. In this work we extend this last result to prove that in fact it is possible to derive a monoparametric family of metrics from the classical Jensen-Shannon divergence. Motivated by our results, an application into the field of symbolic sequences segmentation is explored. Additionally, we analyze the possibility to extend this result into the quantum realm.

math-ph↗

arXiv2017

Distinguishability notion based on Wootters statistical distance: application to discrete maps

We study the distinguishability notion given by Wootters for states represented by probability density functions. This presents the particularity that it can also be used for defining a distance in chaotic unidimensional maps. Based on that definition, we provide a metric $\overline{d}$ for an arbitrary discrete map. Moreover, from this we associate a metric space to each invariant density of a given map, which results to be the set of all distinguished points when the number of iterations of the map tends to infinity. Also, we give a characterization of the wandering set of a map in terms of the given metric which allows to identify the dissipative regions in the phase space. We illustrate the results in the case of the logistic and the circle maps numerically and theoretically, and we obtain the metric and the wandering set for some characteristic values of their parameters.

nlin.CD↗

arXiv2013

Purification-based metric to measure the distance between quantum states and processes

In this work we study the properties of an purification-based entropic metric for measuring the distance between both quantum states and quantum processes. This metric is defined as the square root of the entropy of the average of two purifications of mixed quantum states which maximize the overlap between the purified states. We analyze this metric and show that it satisfies many appealing properties, which suggest this metric is an interesting proposal for theoretical and experimental applications of quantum information.

quant-ph↗

arXiv2006

A complexity measure for symbolic sequences and applications to DNA

We introduce a complexity measure for symbolic sequences. Starting from a segmentation procedure of the sequence, we define its complexity as the entropy of the distribution of lengths of the domains of relatively uniform composition in which the sequence is decomposed. We show that this quantity verifies the properties usually required for a ``good'' complexity measure. In particular it satisfies the one hump property, is super-additive and has the important property of being dependent of the level of detail in which the sequence is analyzed. Finally we apply it to the evaluation of the complexity profile of some genetic sequences.

physics.class-ph↗

arXiv2000

A nonextensive critical phenomenon scenario for quantum entanglement

We discuss the paradigmatic bipartite spin-1/2 system having the probabilities $\frac{1+3x}{4}$ of being in the Einstein-Podolsky-Rosen fully entangled state $|Ψ^-$$> \equiv \frac{1}{\sqrt 2}(|$$\uparrow>_A|$$\downarrow>_B$$-|$$\downarrow>_A|$$\uparrow>_B)$ and $\frac{3(1-x)}{4}$ of being orthogonal. This system is known to be separable if and only if $x\le1/3$ (Peres criterion). This critical value has been recently recovered by Abe and Rajagopal through the use of the nonextensive entropic form $S_q \equiv \frac{1- Tr ρ^q}{q-1} (q \in \cal{R}; $$S_1$$= -$ $Tr$ $ ρ\ln ρ)$ which has enabled a current generalization of Boltzmann-Gibbs statistical mechanics. This result has been enrichened by Lloyd, Baranger and one of the present authors by proposing a critical-phenomenon-like scenario for quantum entanglement. Here we further illustrate and discuss this scenario through the calculation of some relevant quantities.

cond-mat.stat-mech↗