arXiv subjects

K. M. Fonseca-Romero

Publications and source records attributed to K. M. Fonseca-Romero.

11 recordsLinked to original sources

arXiv2024

A quantum treatment of the Stern-Gerlach experiment

Most textbooks introduce the concept of spin by presenting the Stern-Gerlach experiment with the aid of Newtonian atomic trajectories. However, to understand how both spatial and spin degrees of freedom evolve over time and how the latter influence experimental outcomes, it is essential to employ a quantum approach. In this paper, we offer two simple methods, the Baker-Campbell-Hausdorff formula and the direct integration of the Schrödinger equation in an interaction picture, to determine the corresponding evolution operator. We not only provide an interpretation of the individual terms within this operator but also establish connections with semiclassical calculations, when feasible. Moreover, we compute the wave function and touch upon the concept of position-spin entanglement to illustrate how a full quantum description of the Stern-Gerlach experiment can open doors to topics like quantum measurement and nonlocality.

quant-ph↗

arXiv2023

Classical models may be a better explanation of the Jiuzhang 1.0 Gaussian Boson Sampler than its targeted squeezed light model

Recently, Zhong et al. performed landmark Gaussian boson sampling experiments with up to 144 modes using threshold detectors. The authors claim to have achieved quantum computational advantage with the implementation of these experiments, named Jiuzhang 1.0 and Jiuzhang 2.0. Their experimental results are validated against several classical hypotheses and adversaries using tests such as the comparison of statistical correlations between modes, Bayesian hypothesis testing and the Heavy Output Generation (HOG) test. We propose an alternative classical hypothesis for the validation of these experiments using the probability distribution of mixtures of coherent states sent into a lossy interferometer; these input mixed states, which we term squashed states, have vacuum fluctuations in one quadrature and excess fluctuations in the other. We find that for configurations in the high photon number density regime, the comparison of statistical correlations does not tell apart the ground truth of the experiment (two-mode squeezed states sent into an interferometer) from our alternative hypothesis. The Bayesian test indicates that, for all configurations excepting Jiuzhang 1.0, the ground truth is a more likely explanation of the experimental data than our alternative hypothesis. A similar result is obtained for the HOG test: for all configurations of Jiuzhang 2.0, the test indicates that the experimental samples have higher ground truth probability than the samples obtained form our alternative distribution; for Jiuzhang 1.0 the test is inconclusive. Our results provide a new hypothesis that should be considered in the validation of future GBS experiments, and shed light into the need to identify proper metrics to verify quantum advantage in the context of GBS. They also indicate that a classical explanation of the Jiuzhang 1.0 experiment, lacking any quantum features, has not been ruled out.

quant-ph↗

arXiv2023

Partial and complete qubit estimation using a single observable: optimization and quantum simulation

Quantum state estimation is an important task of many quantum information protocols. We consider two families of unitary evolution operators, one with a one-parameter and the other with a two-parameter, which enable the estimation of a single spin component and all spin components, respectively, of a two-level quantum system. To evaluate the tomographic performance, we use the quantum tomographic transfer function (qTTF), which is calculated as the average over all pure states of the trace of the inverse of the Fisher information matrix. Our goal is to optimize the qTTF for both estimation models. We find that the minimum qTTF for the one-parameter model is achieved when the entangling power of the corresponding unitary operator is at its maximum. The models were implemented on an IBM quantum processing unit, and while the estimation of a single-spin component was successful, the whole spin estimation displayed relatively large errors due to the depth of the associated circuit. To address this issue, we propose a new scalable circuit design that improves qubit state tomography when run on an IBM quantum processing unit.

quant-ph↗

arXiv2021

Spin-state estimation using the Stern-Gerlach experiment

We propose a state estimation scheme for spins, using a modified setup of the Stern-Gerlach experiment, in which a beam of neutral spin-1/2 point particles interacts with a quadrupolar magnetic field. The proposed linear inversion estimation procedure, based on a quadrant intensity detector, requires a suitable initial spatial state of the beam. The statistical characterization of the estimator of the initial spin state allows us not only to associate an error to the estimated parameters, but also to define a measure for comparing estimation procedures corresponding to different Stern-Gerlach setups.

quant-ph↗

arXiv2017

Single plane minimal tomography of double slit qubits

The determination of the density matrix of an ensemble of identically prepared quantum systems by performing a series of measurements, known as quantum tomography, is minimal when the number of outcomes is minimal. The most accurate minimal quantum tomography of qubits, sometimes called a tetrahedron measurement, corresponds to projections over four states which can be represented on the Bloch sphere as the vertices of a regular tetrahedron. We investigate whether it is possible to implement the tetrahedron measurement of double slit qubits of light, using measurements performed on a single plane. Assuming Gaussian slits and free propagation, we demonstrate that a judicious choice of the detection plane and the double slit geometry allows the implementation of a tetrahedron measurement. Finally, we consider possible sets of values which could be used in actual experiments.

quant-ph↗

arXiv2014

Anisotropic Dirac cones in monatomic hexagonal lattices

In the last few years, the fascinating properties of graphene have been thoroughly investigated. The existence of Dirac cones is the most important characteristic of the electronic band-structure of graphene. In this theoretical paper, hexagonal monolayers of silicon (h-Si) and germanium (h-Ge) are examined using density functional theory, within the generalized gradient approximation. Our numerical results indicate that both h-Si and h-Ge are chemically stable. The lattice parameters, electronic dispersion relations and densities of states for these systems are reported. The electronic dispersion relations display Dirac cones with the symmetry of an equilateral triangle (the group D$_3$) in the vicinity of the K points. Hence, the Fermi velocity depends on the wave vector direction around $K$ points. Fermi velocities for holes and electrons are significantly different. The maximum and minimum Fermi velocities are also reported.

cond-mat.mes-hall↗

arXiv2012

Can the exciton--polariton regime be defined by its quantum properties?

Using a simple fully quantum model in an effective exciton scheme that takes into account the system--environment interaction, we study the different regimes arising in a microcavity--quantum dot system. Our numerical calculations of the emission linewidth, emission energy, integrated intensity and second- and third-order correlation functions are in good qualitative agreement with reported experimental results. We show that the transition from the polariton-laser to the photon-laser regime can be defined through the critical points of both the negativity and the linear entropy of the steady state.

cond-mat.mes-hall↗

arXiv2010

Decoherence and entanglement in tripartite systems: Cavity QED

We propose an experimental setup, feasible with present day technology, involving two highquality- factor cavities, one Ramsey zone and a two-level atom which interacts with them. The dynamics in the cavities is modeled by a dissipative dispersive Jaynes-Cummings model. Analytical expresions for the evolution superoperator in each part of the proposed setup and for the concurrence between the atom and the first cavity are given, and the pairwise entanglement of the subsystems is calculated numerically. We consider initial separable states given by the tensor product of a superposition of the two atomic relevant states and coherent states for the fields. We show that for realistic model parameters (including dissipation), when the dissipation rates are smaller than the dispersive frequencies (the ratio between the squared vacuum Rabi frequencies and the detunings), the final state of the cavity fields remains entangled.

quant-ph↗

arXiv2008

Damped driven coupled oscillators: entanglement, decoherence and the classical limit

The interaction of (two-level) Rydberg atoms with dissipative QED cavity fields can be described classically or quantum mechanically, even for very low temperatures and mean number of photons, provided the damping constant is large enough. We investigate the quantum-classical border, the entanglement and decoherence of an analytically solvable model, analog to the atom-cavity system, in which the atom (field) is represented by a (driven and damped) harmonic oscillator. The maximum value of entanglement is shown to depend on the initial state and the dissipation-rate to coupling-constant ratio. While in the original model the atomic entropy never grows appreciably (for large dissipation rates), in our model it reaches a maximum before decreasing. Although both models predict small values of entanglement and dissipation, for fixed times of the order of the inverse of the coupling constant and large dissipation rates, these quantities decrease faster, as a function of the ratio of the dissipation rate to the coupling constant, in our model.

quant-ph↗

arXiv2002

Optimal Control of One-Qubit Gates

We consider the problem of carrying an initial Bloch vector to a final Bloch vector in a specified amount of time under the action of three control fields (a vector control field). We show that this control problem is solvable and therefore it is possible to optimize the control. We choose the physically motivated criteria of minimum energy spent in the control, minimum magnitude of the rate of change of the control and a combination of both. We find exact analytical solutions.

quant-ph↗

arXiv2002

Sensitivity to Initial Conditions in Quantum Dynamics: an Analytical Semiclassical Expansion

We construct a class of systems for which quantum dynamics can be expanded around a mean field approximation with essentially classical content. The modulus of the quantum overlap of mean field states naturally introduces a classical distance between classical phase points. Using this fact we analytically show that the time rate of change (trc) of two neighbouring classical trajectories is directly proportional to the trc of quantum correlations. Coherence loss and nonlocality effects appear as corrections to mean field dynamics and we show that they can be given in terms of classical trajectories and generalized actions. This result is a first step in the connection between quantum and classically chaotic dynamics in the same sense of semiclassical expansions for the density of states. We apply the results to the nonintegrable (classically chaotic) version of the N-atom Jaynes-Cummings model.

quant-ph↗