arXiv subjects

Alex E. Bernardini

Publications and source records attributed to Alex E. Bernardini.

At least 37 records · Page 2Linked to original sources

arXiv2021

Intrinsic quantum correlations for Gaussian localized Dirac cat states in phase space

Following the information-based approach to Dirac spinors under a constant magnetic field, the phase-space representation of symmetric and anti-symmetric localized Dirac cat states is obtained. The intrinsic entanglement profile implied by the Dirac Hamiltonian is then investigated so as to shed a light on quantum states as carriers of qubits correlated by phase-space variables. Corresponding to the superposition of Gaussian states, cat states exhibit non-trivial elementary information dynamics which include the interplay between intrinsic entanglement and quantum superposition as reported by the corresponding Dirac archetypes. Despite the involved time-evolution as non-stationary states, the Wigner function constrains the elementary information quantifiers according to a robust framework which can be consistently used for quantifying the time-dependent $SU(2) \otimes SU(2)$ (spin projection and intrinsic parity) correlation profile of phase-space localized Dirac spinor states. Our results show that the Dirac Wigner functions for cat states -- described in terms of generalized Laguerre polynomials -- exhibit an almost maximized timely persistent mutual information profile which is engendered by either classical- or quantum-like spin-parity correlations, depending on the magnetic field intensity.

quant-ph↗

arXiv2021

Chiral oscillations in the non-relativistic regime

Massive Dirac particles are a superposition of left and right chiral components. Since chirality is not a conserved quantity, the free Dirac Hamiltonian evolution induces chiral quantum oscillations, a phenomenon related to the \textit{Zitterbewegung}, the trembling motion of free propagating particles. While not observable for particles in relativistic dynamical regimes, chiral oscillations become relevant when the particle's rest energy is comparable to its momentum. In this paper, we quantify the effect of chiral oscillations on the non-relativistic evolution of a particle state described as a Dirac bispinor and specialize our results to describe the interplay between chiral and flavor oscillations of non-relativistic neutrinos: we compute the time-averaged survival probability and observe an energy-dependent depletion of the quantity when compared to the standard oscillation formula. In the non-relativistic regime, this depletion due to chiral oscillations can be as large as 40$\%$. Finally, we discuss the relevance of chiral oscillations in upcoming experiments which will probe the cosmic neutrino background.

hep-ph↗

arXiv2020

Classical and statistical limits of the quantum singular oscillator

The classical boundaries of the quantum singular oscillator (SO) is addressed under Weyl-Wigner phase-space and Bohmian mechanics frameworks as to comparatively evaluate phase-space and configuration space quantum trajectories as well as to compute distorting quantum fluctuations. For an engendered pure state \textit{quasi}-gaussian Wigner function that recovers the classical time evolution (at phase and configuration spaces), Bohmian trajectories are analytically obtained as to show how the SO energy and anharmonicity parameters drive the quantum regime through the so-called quantum force, which quantitatively distorts the recovered classical behavior. Extending the discussion of classical-quantum limits to a quantum statistical ensemble, the thermalized Wigner function and the corresponding Wigner currents are computed as to show how the temperature dependence affects the local quantum fluctuations. Considering that the level of quantum mixing is quantified by the quantum purity, the loss of information is quantified in terms of the temperature effects. Despite having contrasting phase-space flow profiles, two inequivalent quantum systems, namely the singular and the harmonic oscillators, besides reproducing stable classical limits, are shown to be statistically equivalent at thermal equilibrium, a fact that raises the SO non-linear system to a very particular category of quantum systems.

quant-ph↗

arXiv2020

Anharmonic effects on phase-space quantum profiles: an exact approach

Given its well known spectral decomposition profile, the $1$-dim harmonic oscillator potential modified by an inverse square ($1$-dim angular momentum-like) contribution works as an efficient platform for probing classical and quantum information quantifiers in the context of the phase-space Weyl-Wigner formalism. In particular, the phase-space informational content related to the canonical ensemble driven by such a {\em singular oscillator} can be quantified in terms of well established analytical structures. Considering that, on one hand, the {\em singular oscillator} produce a spectral decomposition profile equivalent to that one of the unmodified harmonic system -- in the sense that they result into identical thermodynamic statistics, even for different statistical mixtures -- on the other hand, a more complete scrutinization of their phase-space information content can capture some different aspects of the encoded information for the related quantum ensembles. Besides the identification of decoherence effects, the Wigner flow analysis is presumedly useful in identifying stable quantum configurations, according to finite temperature and interaction parameter values. Unexpectedly, our results show that the equivalence between the statistical (quantum) mechanics of the anharmonic singular oscillator and an ordinary harmonic oscillator can also be extended to the phase-space quantum purity quantifier, which is analytically computed and reproduces exactly the same quantum ensemble statistical mixture profile, which does not depend on interaction parameter values.

quant-ph↗

arXiv2020

Phase-space elementary information content of confined Dirac spinors

Reporting about the Wigner formalism for describing Dirac spinor structures through a covariant phase-space formulation, the quantum information quantifiers for purity and mutual information involving spin-parity (discrete) and position-momentum (continuous) degrees of freedom are consistently obtained. For Dirac spinor Wigner operators decomposed into Poincaré classes of $SU(2) \otimes SU(2)$ spinor couplings, a definitive expression for quantum purity is identified in a twofold way: firstly, in terms of phase-space positively defined quantities, and secondly, in terms of the {\em spin-parity traced-out} associated density matrix in the position coordinate representation, both derived from the original Lorentz covariant phase-space Wigner representation. Naturally, such a structure supports the computation of relative (linear) entropies respectively associated to discrete (spin-parity) and continuous (position-momentum) degrees of freedom. The obtained theoretical tools are used for quantifying (relative) purities, mutual information as well as, by means of the quantum concurrence quantifier, the spin-parity quantum entanglement, for a charged fermion trapped by a uniform magnetic field which, by the way, has the phase-space structure completely described in terms of Laguerre polynomials associated to the quantized Landau levels. Our results can be read as the first step in the systematic computation of the elementary information content of Dirac-like systems exhibiting some kind of confining behavior.

quant-ph↗

arXiv2020

On the elementary information content of thermodynamic ensembles

Extending the definition of phase-space (Wigner) quantum projectors to thermodynamic ensembles usually results into an efficient platform for quantifying their elementary information content. Given the spectral decomposition profile of a thermalized quantum system, general expressions for the quantum purity quantifier, $\mathcal{P}(β)$, and for phase-space projectors related to the quantum fidelity, $\mathcal{F}(β)$, are explicitly derived in terms of an explicit correspondence with the related partition function, $\mathcal{Z}(β)$. Besides quantifying the storage of information capacity of thermodynamical ensembles, the tools here introduced extend the role of the partition function in expressing the quantum behavior of thermodynamic ensembles.

quant-ph↗

arXiv2020

Lorentz Invariant Quantum Concurrence for SU(2) x SU(2) spin-parity states

The quantum concurrence of $SU(2) \otimes SU(2)$ spin-parity states is shown to be invariant under $SO(1,3)$ Lorentz boosts and $O(3)$ rotations when the density matrices are constructed in consonance with the covariant probabilistic distribution of Dirac massive particles. Similar invariance properties are obtained for the quantum purity and for the trace of unipotent density matrix operators. The reported invariance features -- obtained in the scope of the $SU(2) \otimes SU(2)$ corresponding to just one of the inequivalent representations enclosed by the $SL(2,\mathbb{C})\otimes SL(2,\mathbb{C})$ symmetry -- set a more universal and kinematical-independent meaning for the quantum entanglement encoded in systems containing not only information about spin polarization but also the correlated information about intrinsic parity. Such a covariant framework is used for computing the Lorentz invariant spin-parity entanglement of spinorial particles coupled to a magnetic field, through which the extensions to more general Poincaré classes of spinor interactions are straightforwardly depicted.

quant-ph↗

arXiv2019

Cosmological comoving behavior of the configurational entropy

It has been shown that a functional dependence of the configurational entropy (CE) density exhibits a cosmological comoving behavior related to the scale parameter, $a$, of the FRW flat universe. Such a circumstantial comoving behavior shows that the CE evolves with $a^{-3}$ for fermionic and bosonic radiation and with $a^{-3/2}$ for non-relativistic fermionic matter. The results are discussed in the domain of matter and radiation, as well as in a simplified context of the $Λ$CDM cosmology. Our results suggest that the CE can work as a theoretical driver for particle and nuclear interactions in the context of large scale cosmic events.

gr-qc↗

arXiv2019

Phase-space continuity equations for quantum decoherence, purity, von Neumann and Rényi entropies

Phase-space features of the Wigner flow are examined so to provide a set of continuity equations that describe the flux of quantum information in the phase-space. The reported results suggest that the non-classicality profile of anharmonic (periodic) quantum systems can be consistently obtained in terms of the fluxes of probability, purity and von Neumann entropy. Extensions of the such phase-space quantifiers are also investigated in the context of the so-called Rényi entropy.

quant-ph↗

arXiv2018

Testing non-classicality with exact Wigner currents for an anharmonic quantum system

Phase-space features of the Wigner flow for an anharmonic quantum system driven by the harmonic oscillator potential modified by the addition of an inverse square (one-dimension Coulomb-like) contribution are analytically described in terms of Wigner functions and Wigner currents. Reporting about three correlated continuity equations which quantify the flux of quantum information in the phase-space, the non-classicality profile of such an anharmonic system can be consistently obtained in terms of the fluxes of {\em probability}, {\em purity} and {\em von Neumann-like entropy}. Considering that quantum fluctuations can be identified from distortions over the classical regime, they can be quantified through the above-mentioned information fluxes whenever some {\em classically bounded} volume of the phase-space is selected. Our results suggest that the Wigner flow approach works as a probe of quantumness and classicality for a large set of anharmonic quantum systems driven by quantum wells.

quant-ph↗

arXiv2018

Effects of Lorentz boosts on Dirac bispinor entanglement

In this paper we describe the transformation properties of quantum entanglement encoded in a pair of spin 1/2 particles described via Dirac bispinors. Due to the intrinsic parity-spin internal structure of the bispinors, the joint state is a four-qubit state exhibiting multipartite entanglement, and to compute global correlation properties we consider the averaged negativities over each possible bi-partition. We also consider specific bipartitions, such as the spin-spin and the particle-particle bipartitions. The particle-particle entanglement, between all degrees of freedom of one particle and all degrees of freedom of the other particle, is invariant under boosts if each particle has a definite momentum, although the spin-spin entanglement is degraded for high speed boosts. Correspondingly, the mean negativities are not invariant since the boost drives changes into correlations encoded in specific bipartitions. Finally, the results presented in the literature about spin-momentum entanglement are recovered by considering the projection of bispinorial states into positive intrinsic parity, and some striking differences between the appropriate approach for this case and the one usually treated in the literature are discussed.

quant-ph↗

arXiv2018

Phase-space quantum profile of Pöschl-Teller two-level systems

The quantum phase-space dynamics driven by hyperbolic Pöschl-Teller (PT) potentials is investigated in the context of the Weyl-Wigner quantum mechanics. The obtained Wigner functions for quantum superpositions of ground and first-excited states exhibit some non-classical and non-linear patterns which are theoretically tested and quantified according to a non-gaussian continuous variable framework. It comprises the computation of quantifiers of non-classicality for an anharmonic two-level system where non-Liouvillian features are identified through the phase-space portrait of quantum fluctuations. In particular, the associated non-gaussian profiles are quantified by measures of {\em kurtosis} and {\em negative entropy}. As expected from the PT {\em quasi}-harmonic profile, our results suggest that quantum wells can work as an experimental platform that approaches the gaussian behavior in the investigation of the interplay between classical and quantum scenarios. Furthermore, it is also verified that the Wigner representation admits the construction of a two-particle bipartite quantum system of continuous variables, $A$ and $B$, identified by $\sum_{i,j=0,1}^{i\neq j}\vert i_{_A}\rangle\otimes\vert j_{_B}\rangle$, which are shown to be separable under gaussian and non-gaussian continuous variable criteria.

quant-ph↗

arXiv2018

Global Dirac bispinor entanglement under Lorentz boosts

The effects of Lorentz boosts on the quantum entanglement encoded by a pair of massive spin one-half particles are described according to the Lorentz covariant structure described by Dirac bispinors. The quantum system considered incorporates four degrees of freedom -- two of them related to the bispinor intrinsic parity and other two related to the bispinor spin projection, i.e. the Dirac particle helicity. Because of the natural multipartite structure involved, the Meyer-Wallach global measure of entanglement is preliminarily used for computing global quantum correlations, while the entanglement separately encoded by spin degrees of freedom is measured through the negativity of the reduced two-particle spin-spin state. A general framework to compute the changes on quantum entanglement induced by a boost is developed, and then specialized to describe three particular anti-symmetric two-particle states. According to the obtained results, two-particle spin-spin entanglement cannot be created by the action of a Lorentz boost in a spin-spin separable anti-symmetric state. On the other hand, the maximal spin-spin entanglement encoded by anti-symmetric superpositions is degraded by Lorentz boosts driven by high-speed frame transformations. Finally, the effects of boosts on chiral states are shown to exhibit interesting invariance properties, which can only be obtained through such a Lorentz covariant formulation of the problem.

quant-ph↗

arXiv2018

Graphene lattice-layer entanglement under non-Markovian phase noise

The evolution of single particle excitations of bilayer graphene under effects of non-Markovian noise is described with focus on the decoherence process of lattice-layer (LL) maximally entangled states. Once that the noiseless dynamics of an arbitrary initial state is identified by the correspondence between the tight-binding Hamiltonian for the AB-stacked bilayer graphene and the Dirac equation -- which includes pseudovector- and tensor-like field interactions -- the noisy environment is described as random fluctuations on bias voltage and mass terms. The inclusion of noisy dynamics reproduces the Ornstein-Uhlenbeck processes: a non-Markovian noise model with a well-defined Markovian limit. Considering that an initial amount of entanglement shall be dissipated by the noise, two profiles of dissipation are identified. On one hand, for eigenstates of the noiseless Hamiltonian, deaths and revivals of entanglement are identified along the oscillation pattern for long interaction periods. On the other hand, for departing LL Werner and Cat states, the entanglement is suppressed although, for both cases, some identified memory effects compete with the pure noise-induced decoherence in order to preserve the the overall profile of a given initial state.

cond-mat.mes-hall↗

arXiv2018

Quantum to classical transition in the Hořava-Lifshitz quantum cosmology

A quasi-Gaussian quantum superposition of Hořava-Lifshitz (HL) stationary states is built in order to describe the transition of the quantum cosmological problem to the related classical dynamics. The obtained HL phase-space superposed Wigner function and its associated Wigner currents describe the conditions for the matching between classical and quantum phase-space trajectories. The matching quantum superposition parameter is associated to the total energy of the classical trajectory which, at the same time, drives the engendered Wigner function to the classical stationary regime. Through the analysis of the Wigner flows, the quantum fluctuations that distort the classical regime can be quantified as a measure of (non)classicality. Finally, the modifications to the Wigner currents due to the inclusion of perturbative potentials are computed in the HL quantum cosmological context. In particular, the inclusion of a cosmological constant provides complementary information that allows for connecting the age of the Universe with the overall stiff matter density profile.

gr-qc↗

arXiv2017

Non-classicality from the phase-space flow analysis of the Weyl-Wigner quantum mechanics

A fluid analog of the information flux in the phase-space associated to purity and von Neumann entropy are identified in the Weyl-Wigner formalism of quantum mechanics. Once constrained by symmetry and positiveness, the encountered continuity equations provide novel quantifiers for non-classicality (non-Liouvillian fluidity) given in terms of quantum decoherence, purity and von Neumann entropy fluxes. Through definitions in the Weyl-Wigner formalism, one can identify the quantum fluctuations that distort the classical-quantum coincidence regime, and the corresponding quantum information profile, whenever some bounded $x-p$ volume of the phase-space is specified. The dynamics of anharmonic systems is investigated in order to illustrate such a novel paradigm for describing quantumness and classicality through the flux of quantum information in the phase-space.

quant-ph↗

arXiv2017

Quantum information aspects of noncommutative quantum mechanics

Some fundamental aspects related with the construction of Robertson-Schrödinger like uncertainty principle inequalities are reported in order to provide an overall description of quantumness, separability and nonlocality of quantum systems in the noncommutative phase-space. Some consequences of the deformed noncommutative algebra are also considered in physical systems of interest.

quant-ph↗

arXiv2017

Dirac bi-spinor entanglement under local noise and its simulation by Jaynes-Cummings interactions

A description of the effects of the local noise on the quantum entanglement constraining the internal degrees of freedom of Dirac bi-spinor structures driven by arbitrary Poincaré invariant potentials is proposed. Given that the Dirac equation dynamics including external potentials can be simulated by a suitable four level trapped ion setup, quantum entanglement of two-qubit ionic states with quantum numbers related to the total angular momentum and to its projection onto the direction of the external magnetic field (used for lift the ions degeneracy), are recovered by means of a suitable ansatz. This formalism allows the inclusion of noise effects, which leads to disentanglement in the four level trapped ion quantum system. Our results indicate the role of interactions in bi-spinor entanglement, as well as the description of disentanglement in ionic states under local noises. For a state prepared initially in one of the ionic levels, local noise induces entanglement sudden death followed by sudden revivals driven by the noiseless dynamics of the state. Residual quantum correlations are observed in the intervals where such state is separable. Schrödinger cat and Werner states partially loose their initial entanglement content due to the interaction with the noisy environment but presenting entanglement oscillations without sudden death. Because Dirac equation describes low energy excitations of mono layer and bi-layer graphene, the formalism can also be applied to compute, for instance, electron-hole or electron/electron entanglement in various circumstances.

quant-ph↗