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Juan M. Romero

Publications and source records attributed to Juan M. Romero.

At least 19 recordsLinked to original sources
arXiv2025

Area and volume as emergent phenomena from entangled qubits

Recently, a connection has been shown between certain geometric quantities and quantum information theory. In this paper, we demonstrate that geometric quantities such as area and volume can emerge directly from entangled multi-qubit states. In particular, the area of a two-dimensional parallelogram is derived from a 4-qubit entangled state, the vector area of a three-dimensional parallelogram from three 6-qubit entangled states, and the volume of a three-dimensional parallelepiped from a 9-qubit entangled state. Corresponding quantum circuits are constructed and implemented using Qiskit to generate the required entangled states. Given that parallelograms and parallelepipeds serve as elementary building blocks for more complex geometric structures, these results may offer a pathway toward exploring emergent geometry in quantum information frameworks

quant-ph↗
arXiv2025

A novel quantum circuit for the quantum Fourier transform

The Quantum Fourier Transform (QFT) is a fundamental component of many quantum computing algorithms. In this paper, we present an alternative method for factoring this transformation. Inspired by this approach, we introduce a new quantum circuit for implementing the QFT. We show that this circuit is more efficient than the conventional design. Furthermore, using this circuit, we develop alternative versions of the HHL algorithm and Shor's algorithm, which also demonstrate improved performance compared to their standard implementations.

quant-ph↗
arXiv2024

Alternative Bell's states and teleportation

Bell's states are among the most useful in quantum computing. These state are an orthonormal base of entagled states with two qubits. We propose alternative bases of entangled states. Some of these states depend on a continuous parameter. We present the quantum circuit and code of these alternative bases. In addition, we study quantum teleportation with these entangled states and present their quantum circuits and codes associated.

quant-ph↗
arXiv2024

Quantum Entanglement, Quantum Teleportation, Multilinear Polynomials and Geometry

We show that quantum entanglement states are associated with multilinear polynomials that cannot be factored. By using these multilinear polynomials, we propose a geometric representation for entanglement states. In particular, we show that the Bell's states are associated with non-factorable real multilinear polynomial, which can be represented geometrically by three-dimensional surfaces. Furthermore, in this framework, we show that a quantum circuit can be seen as a geometric transformations of plane geometry. This phenomenon is analogous to gravity, where matter curves space-time. In addition, we show an analogy between quantum teleportation and operations involving multilinear polynomials.

quant-ph↗
arXiv2021

Snyder and their representation with creation and annihilation operators

Inspired by the Schwinger's representation of angular momentum, we propose a representation of certain operators where we use the algebra of the annihilation and creation operators. In particular, we propose a representation of the Snyder space-time with the help of the annihilation and creation operators, which create and annihilate quantum of space. In addition, we show that by using a matrix representation of the $SO(3)$ or $SU(2)$ Lie algebra it is possible to obtain a representation of the spacial sector of Snyder space-time. Finally, we obtain a quantized expectation value of the area of a sphere.

hep-th↗
arXiv2020

Anisotropic Lifshitz holography in Einstein-Proca theory with stable negative mass spectrum

In this article we focus on constructing a new family of spatially anisotropic Lifshitz spacetimes with arbitrary dynamical exponent z and constant negative curvature in d+1 dimensions within the framework of the Einstein-Proca theory. The constructed metric tensor depends on both the spacetime dimensionality and the critical exponent, while the curvature scalar depends just on the number of dimensions. We also obtained a novel spectrum with negative squared mass that respects the corresponding Breitenlohner-Freedman bound. Hence these new solutions are stable and can be useful within the gravity/condensed matter theory holographic duality, since the spectrum with negative squared mass is complementary to the positive ones already known in the literature.

hep-th↗
arXiv2017

Fractional cable equation for general geometry, a model of axons with swellings and anomalous diffusion

Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as multiple sclerosis, Alzheimer's disease and Parkinson's disease. Indeed, abnormal accumulation of proteins and organelles in axons is a hallmark feature of these diseases. The diffusion in the axons can become to anomalous as a result from this abnormality. In this case the voltage propagation in axons is affected. Another hallmark feature of different neurodegenerative diseases is given by discrete swellings along the axon. In order to model the voltage propagation in axons with anomalous diffusion and swellings, in this paper we propose a fractional cable equation for general geometry. This generalized equation depends on fractional parameters and geometric quantities such as the curvature and torsion of the cable. For a cable with a constant radius we show that the voltage decreases when the fractional effect increases. In cables with swellings we find that when the fractional effect or the swelling radius increase, the voltage decreases. A similar behavior is obtained when the number of swellings and the fractional effect increase. Moreover, we find that when the radius swelling (or the number of swellings) and the fractional effect increase at the same time, the voltage dramatically decreases.

q-bio.NC↗
arXiv2017

Cable equation for general geometry

The cable equation describes the voltage in a straight cylindrical cable, this model has been employed to model electrical potential in dendrites and axons. However, sometimes this equation might give incorrect predictions for some realistic geometries, in particular when the radius of the cable changes significantly. Cables with a non constant radius are important for some phenomena, for example discrete swellings along the axons appear in neurodegenerative diseases such as Alzheimer, Parkinson, HIV-associated dementia and Multiple Sclerosis. In this paper, using the Frenet-Serret frame, we propose a generalized cable equation for a general cable geometry. This generalized equation depends on geometric quantities such as the curvature and torsion of the cable. We show that when the cable has a constant circular cross-section, the first fundamental form of the cable can be simplified and the generalized cable equation depends on neither the curvature nor the torsion of the cable. Additionally, we find an exact solution for an ideal cable which has a particular variable circular cross-section and zero curvature. For this case we show that when the cross-section of the cable increases the voltage decreases. Inspired in this ideal case, we rewrite the generalized cable equation as a diffusion equation with a source term generated by the cable geometry. This source term depends on the cable cross-section area and its derivates. In addition, we study different cables with swelling and provide their numerical solutions. The numerical solutions show that when the cross-section of the cable has abrupt changes, its voltage is smaller than the voltage in the cylindrical cable. Furthermore, these numerical solutions show that the voltage can be affected by geometrical inhomogeneities on the cable.

q-bio.NC↗
arXiv2016

Relativistic Quantum Finance

Employing the Klein-Gordon equation, we propose a generalized Black-Scholes equation. In addition, we found a limit where this generalized equation is invariant under conformal transformations, in particular invariant under scale transformations. In this limit, we show that the stock prices distribution is given by a Cauchy distribution, instead of a normal distribution.

q-fin.MF↗
arXiv2016

Exact solutions for optimal execution of portfolios transactions and the Riccati equation

We propose two methods to obtain exact solutions for the Almgren-Chriss model about optimal execution of portfolio transactions. In the first method we rewrite the Almgren-Chriss equation and find two exact solutions. In the second method, employing a general reparametrized time, we show that the Almgren-Chriss equation can be reduced to some known equations which can be exactly solved in different cases.For this last case we obtain a quantity conserved. In addition, we show that in both methods the Almgren-Chriss equation is equivalent to a Riccati equation.

q-fin.MF↗
arXiv2016

The dengue fever in four municipalities of the Colima state, Mexico, from 2008 to 2015 and its relation with some climatological normals

Although dengue fever is an ancient disease that should have been eradicated since time ago, in Mexico as well as in other regions worldwide the cases of classic and hemorrhagic dengue continue to be reported presently. Since 2002 (and before), a worrying outbreak of dengue was observed in several states of Mexico, notably the case of Colima for which a "descacharrizacion" campaign was implemented in 2009 to encourage the population to get rid of old objects accumulated in their backyards and outdoors so as to prevent proliferation of mosquitoes Aedes Aegypti. To understand the effect of such campaign, we studied the incidence of dengue in four municipalities of the mentioned state, namely Manzanillo, Armeria, Tecoman and Ixtlahuacan. In particular, we observed that the incidence of dengue in these four municipalities had a strong relationship with climatological normals, specifically precipitation and minimum temperature. Furthermore, the results showed that the mentioned campaign helped prevent mosquito eggs incubation and their development, thus leading to reduction of the incidence of dengue in the human population.

q-bio.PE↗
arXiv2015

Lifshitz field theories, Snyder noncomutative space-time and momentum dependent metric

In this work, we propose three different modified relativistic particles. In the first case, we propose a particle with metrics depending on the momenta and we show that the quantum version of these systems includes different field theories, as Lifshitz field theories. As a second case we propose a particle that implies a modified symplectic structure and we show that the quantum version of this system gives different noncommutative space-times, for example the Snyder space-time. In the third case, we combine both structures before mentioned, namely noncommutative space-times and momentum dependent metrics. In this last case, we show that anisotropic field theories can be seen as a limit of noncommutative field theory.

hep-th↗
arXiv2014

Hamiltonian analysis for Lifshitz type Fields

Using the Dirac Method, we study the Hamiltonian consistency for three field theories. First we study the electrodynamics a la Hořava and we show that this system is consistent for an arbitrary dynamical exponent $z.$ Second, we study a Lifshitz type electrodynamics, which was proposed in [1]. For this last system we found that the canonical momentum and the electrical field are related through a Proca type Green function, however this system is consistent. In addition, we show that the anisotropic Yang-Mills theory with dynamical exponent $z=2$ is consistent. Finally, we study a generalized anisotropic Yang-Mills theory and we show that this last system is consistent too.

hep-th↗
arXiv2014

Dendrites and conformal symmetry

Progress toward characterization of structural and biophysical properties of neural dendrites together with recent findings emphasizing their role in neural computation, has propelled growing interest in refining existing theoretical models of electrical propagation in dendrites while advocating novel analytic tools. In this paper we focus on the cable equation describing electric propagation in dendrites with different geometry. When the geometry is cylindrical we show that the cable equation is invariant under the Schrödinger group and by using the dendrite parameters, a representation of the Schrödinger algebra is provided. Furthermore, when the geometry profile is parabolic we show that the cable equation is equivalent to the Schrödinger equation for the 1-dimensional free particle, which is invariant under the Schrödinger group. Moreover, we show that there is a family of dendrite geometries for which the cable equation is equivalent to the Schrödinger equation for the 1-dimensional conformal quantum mechanics.

math-ph↗
arXiv2013

Relativistic conformal symmetry of neural field propagation in the brain

In this paper, we address a neural field equation that characterizes spatio-temporal propagation of a neural population pulse. Due that the human brain is a complex system whose constituents interaction give rise to fundamental states of consciousness and behavior, it is crucial to gain insight into its functioning even at relativistic scales. To this end, we study the action of the relativistic conformal group on the accounted neural field propagation equation. In particular, we obtain an exact solution for the field propagation equation when the space-time is 3 or 4 dimensional. Furthermore, in the 4 dimensional case and the large distance limit, it is shown that the neural population pulse becomes a Yukawa potential.

hep-th↗
arXiv2013

Schrödinger group and quantum finance

Using the one dimensional free particle symmetries, the quantum finance symmetries are obtained. Namely, it is shown that Black-Scholes equation is invariant under Schrödinger group. In order to do this, the one dimensional free non-relativistic particle and its symmetries are revisited. To get the Black-Scholes equation symmetries, the particle mass is identified as the inverse of square of the volatility. Furthermore, using financial variables, a Schrödinger algebra representation is constructed.

physics.gen-ph↗
arXiv2012

Very special relativity as particle in a gauge field and two-time physics

The action for a $(3+1)$-dimensional particle in very special relativity is studied. It is proved that massless particles only travel in effective $(2+1)$-dimensional space-time. It is remarkable that this action can be written as an action for a relativistic particle in a background gauge field and it is shown that this field causes the dimensional reduction. A new symmetry for this system is found. Furthermore, a general action with restored Lorentz symmetry is proposed for this system. It is shown that this new action contains very special relativity and two-time physics.

hep-th↗