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Francisco Marcos de Assis

Publications and source records attributed to Francisco Marcos de Assis.

14 recordsLinked to original sources
arXiv2026

Fixed Point Exploration For CV-QKD IR QC-MET-LDPC Toward Hardware Implementation

High-speed LDPC decoding is a major bottleneck in CV-QKD and motivates hardware acceleration with fixed-point arithmetic. This work compares SPA, MSA, and NMS under a unified low-SNR fixed-point framework using common graph, matrix, and quantization settings. Multiple formats are evaluated through FER, and average iterations. The results show that performance depends strongly on the interaction between decoder rule and numerical precision. SPA achieved the best overall performance. For reduced-complexity decoders, Q16.8 was the lowest consistent precision, with NMS outperforming MSA. Practically, SPA with Q8.4 offered the best balance between reliability and hardware efficiency for large-scale implementations.

cs.AR↗
arXiv2023

Convergence of Density Operators and Security of Discrete Modulated CVQKD Protocols

This communication deals with the problem of bounding the approximation error on weak convergence of mixed coherent state towards a Gaussian thermal state. In the context of CVQKD with discrete modulation, we develop expressions for two specific cases. The first one is the distance between the Gaussian equivalent bipartite state and a reference Gaussian modulated (GG02) and the second one is for the trace distance between the constellation and a thermal state with same photon number. Since, in the convex set of density operators, weak convergence implies convergence in the trace norm, knowing how fast the sequence gets close to the equivalent Gaussian state has implication on the security of QKD Protocols. Here we derive two bounds on the $L_1$ distance, one of them related with an energy test that can be used in the security proof.

quant-ph↗
arXiv2023

A method for Sampling Bernoulli Variables

We introduce new method for generating correlated or uncorrelated Bernoulli random variables by using the binary expansion of a continuous random variable with support on the unit interval. We show that when this variable has a symmetric probability density function around 12 , its binary expansion provides equiprobable bits over {0, 1}. In addition we prove that when the random variable is uniformly distributed over [0, 1], its binary expansion generates independent Bernoulli random variables. Moreover, we give examples where, by choosing some parameterized nonuniform probability density functions over [0, 1], samples of Bernoulli variables with specific correlation values are generated.

math.PR↗
arXiv2023

Converging State Distributions for Discrete Modulated CVQKD Protocols

Consider the problem of using a finite set of coherent states to distribute secret keys over a quantum channel. It is known that computing the exact secret key rate in this scenario is intractable due to the infinite dimensionality of the Hilbert spaces and usually one computes a lower bound using a Gaussian equivalent bipartite state in the entangled based version of the protocol, which leads to underestimating the actual protocol capability of generating secret keys for the sake of security. Here, we define the QKD protocol's non-Gaussianity, a function quantifying the amount of secret key rate lost due to assuming a Gaussian model when a non-Gaussian modulation was used, and develop relevant properties for it. We show that if the set of coherent states is induced by a random variable approaching the AWGN channel capacity, then the protocol's non-Gaussianity vanishes, meaning that there is no loss of secret key rate due to the use of a Gaussian model for computing bound on the secret key rate. The numerical results show that by using a 256-QAM with Gauss-Hermite shaping, the loss of secret key rate quickly falls below $10^{-5}$ as the distance increases.

quant-ph↗
arXiv2023

Distributional Transform Based Information Reconciliation

In this paper, we present an information reconciliation protocol designed for Continuous-Variable QKD using the Distributional Transform. By combining tools from copula and information theory, we present a method for extracting independent symmetric Bernoulli bits for Gaussian-modulated CVQKD protocols, which we called the Distributional Transform Expansion (DTE). We derived the expressions for the maximum reconciliation efficiency for both homodyne and heterodyne measurements, which, for the last, is achievable with an efficiency greater than 0.9 at a signal-to-noise ratio lower than -3.6 dB.

cs.IT↗
arXiv2022

Amplitude-Phase Modulated CVQKD Protocol

Here we report the performance of a discrete modulated Continuous Variable Quantum Key Distribution protocol based on eight and sixteen state optimal Amplitude Phase Keying constellations with pure loss quantum channel transmission. Our constellations use the same amplitudes and state probability as in an optimal four-state unidimensional constellation model and apply amplitude/phase modulation to the quadratures of coherent states. We compare the obtained results with the performance of conventional $m$-PSK and $m$-APK constellations. The results presented show that protocols that use the proposed constellations outperform the ones based on conventional constellations in both secret key rate and link distance. In special, our protocol is able to accomplish viable SKR's in low transmittance regime, $τ<0.2$.

quant-ph↗
arXiv2021

Evaluating the Eavesdropper Entropy via Bloch-Messiah Decomposition

We explore the Bloch-Messiah decomposition of Gaussian unitary to analyze the Entangling Cloner Attack performed by an eavesdropper on a discrete modulated continuous variable QKD scenario. Such a decomposition allows to replace the nonlinear unitary resulting from eavesdropping and tracing out Bob's mode into an architecture of single-mode operations (squeezers, phase shifters and displacements) and a two-mode beam splitter. Based on such architecture we were able to get tighter upper bounds to the eavesdropper entropy for a discrete modulated CVQKD scheme. The new bounds are justified from the Gaussian extremality property valid for entangled-based equivalent protocols.

quant-ph↗
arXiv2019

Entanglement-assisted Quantum Codes from Algebraic Geometry Codes

Quantum error correcting codes play the role of suppressing noise and decoherence in quantum systems by introducing redundancy. Some strategies can be used to improve the parameters of these codes. For example, entanglement can provide a way for quantum error correcting codes to achieve higher rates than the one obtained via the traditional stabilizer formalism. Such codes are called entanglement-assisted quantum (QUENTA) codes. In this paper, we use algebraic geometry codes to construct several families of QUENTA codes via the Euclidean and the Hermitian construction. Two of the families created have maximal entanglement and have quantum Singleton defect equal to zero or one. Comparing the other families with the codes with the respective quantum Gilbert-Varshamov bound, we show that our codes have a rate that surpasses that bound. At the end, asymptotically good towers of linear complementary dual codes are used to obtain asymptotically good families of maximal entanglement QUENTA codes. Furthermore, a simple comparison with the quantum Gilbert-Varshamov bound demonstrates that using our construction it is possible to create an asymptotically family of QUENTA codes that exceeds this bound.

cs.IT↗
arXiv2017

Avaliação do método dialético na quantização de imagens multiespectrais

The unsupervised classification has a very important role in the analysis of multispectral images, given its ability to assist the extraction of a priori knowledge of images. Algorithms like k-means and fuzzy c-means has long been used in this task. Computational Intelligence has proven to be an important field to assist in building classifiers optimized according to the quality of the grouping of classes and the evaluation of the quality of vector quantization. Several studies have shown that Philosophy, especially the Dialectical Method, has served as an important inspiration for the construction of new computational methods. This paper presents an evaluation of four methods based on the Dialectics: the Objective Dialectical Classifier and the Dialectical Optimization Method adapted to build a version of k-means with optimal quality indices; each of them is presented in two versions: a canonical version and another version obtained by applying the Principle of Maximum Entropy. These methods were compared to k-means, fuzzy c-means and Kohonen's self-organizing maps. The results showed that the methods based on Dialectics are robust to noise, and quantization can achieve results as good as those obtained with the Kohonen map, considered an optimal quantizer.

cs.CV↗
arXiv2017

Dialectical Multispectral Classification of Diffusion-Weighted Magnetic Resonance Images as an Alternative to Apparent Diffusion Coefficients Maps to Perform Anatomical Analysis

Multispectral image analysis is a relatively promising field of research with applications in several areas, such as medical imaging and satellite monitoring. A considerable number of current methods of analysis are based on parametric statistics. Alternatively, some methods in Computational Intelligence are inspired by biology and other sciences. Here we claim that Philosophy can be also considered as a source of inspiration. This work proposes the Objective Dialectical Method (ODM): a method for classification based on the Philosophy of Praxis. ODM is instrumental in assembling evolvable mathematical tools to analyze multispectral images. In the case study described in this paper, multispectral images are composed of diffusion-weighted (DW) magnetic resonance (MR) images. The results are compared to ground-truth images produced by polynomial networks using a morphological similarity index. The classification results are used to improve the usual analysis of the apparent diffusion coefficient map. Such results proved that gray and white matter can be distinguished in DW-MR multispectral analysis and, consequently, DW-MR images can also be used to furnish anatomical information.

cs.CV↗
arXiv2017

Fuzzy-Based Dialectical Non-Supervised Image Classification and Clustering

The materialist dialectical method is a philosophical investigative method to analyze aspects of reality. These aspects are viewed as complex processes composed by basic units named poles, which interact with each other. Dialectics has experienced considerable progress in the 19th century, with Hegel's dialectics and, in the 20th century, with the works of Marx, Engels, and Gramsci, in Philosophy and Economics. The movement of poles through their contradictions is viewed as a dynamic process with intertwined phases of evolution and revolutionary crisis. In order to build a computational process based on dialectics, the interaction between poles can be modeled using fuzzy membership functions. Based on this assumption, we introduce the Objective Dialectical Classifier (ODC), a non-supervised map for classification based on materialist dialectics and designed as an extension of fuzzy c-means classifier. As a case study, we used ODC to classify 181 magnetic resonance synthetic multispectral images composed by proton density, $T_1$- and $T_2$-weighted synthetic brain images. Comparing ODC to k-means, fuzzy c-means, and Kohonen's self-organized maps, concerning with image fidelity indexes as estimatives of quantization distortion, we proved that ODC can reach almost the same quantization performance as optimal non-supervised classifiers like Kohonen's self-organized maps.

cs.CV↗
arXiv2015

Quantum Decoding with Venn Diagrams

The quantum error correction theory is as a rule formulated in a rather convoluted way, in comparison to classical algebraic theory. This work revisits the error correction in a noisy quantum channel so as to make it intelligible to engineers. An illustrative example is presented of a naive perfect quantum code (Hamming-like code) with five-qubits for transmitting a single qubit of information. Also the (9,1)-Shor codes is addressed.

cs.IT↗
arXiv2011

Quantum Communication Complexity of Quantum Authentication Protocols

In order to perform Quantum Cryptography procedures it is often essencial to ensure that the parties of the communication are authentic. Such task is accomplished by quantum authentication protocols which are distributed algorithms based on the intrinsic properties of Quantum Mechanics. The choice of an authentication protocol must consider that quantum states are very delicate and that the channel is subject to eavesdropping. However, even in face of the various existing definitions of quantum authentication protocols in the literature, little is known about them in this perspective, and this lack of knowledge may unfavor comparisons and wise choices. In the attempt to overcome this limitation, in the present work we aim at showing an approach to evaluate quantum authentication protocols based on the determination of their quantum communication complexity. Based on our investigation, no similar methods to analyze quantum authentication protocols were found in the literature. Pursuing this further, our approach has advantages that need to be highlighted: it characterizes a systematic procedure to evaluate quantum authentication protocols; its evaluation is intuitive, based only on the protocol execution; the resulting measure is a concise notation of what resources a quantum authentication protocol demands and how many communications are performed; it allows comparisons between protocols; it makes possible to analyze the communication effort when an eavesdropping occurs; and, lastly, it is likely to be applied in almost any quantum authentication protocol. To illustrate the proposed approach, we also bring results about its application in ten existing quantum authentication protocols (data origin authentication and identity authentication). Such evaluations increase the knowledge about the existing protocols, presenting its advantages, limitations and contrasts.

cs.IT↗