arXiv subjects

J. L. Romero

Publications and source records attributed to J. L. Romero.

At least 19 recordsLinked to original sources

arXiv2024

Optimizing measurement tradeoffs in multiparameter spatial superresolution

The quantum Cramér-Rao bound for the joint estimation of the centroid and the separation between two incoherent point sources cannot be saturated. As such, the optimal measurements for extracting maximal information about both at the same time are not known. In this work, we ascertain these optimal measurements for an arbitrary point spread function, in the most relevant regime of a small separation between the sources. Our measurement can be adjusted within a set of tradeoffs, allowing more information to be extracted from the separation or the centroid while ensuring that the total information is the maximum possible.

quant-ph↗

arXiv2024

Multipoles from Majorana constellations

Majorana stars, the $2S$ spin coherent states that are orthogonal to a spin-$S$ state, offer an elegant method to visualize quantum states, disclosing their intrinsic symmetries. These states are naturally described by the corresponding multipoles. These quantities can be experimentally determined and allow for an SU(2)-invariant analysis. We investigate the relationship between Majorana constellations and state multipoles, thus providing insights into the underlying symmetries of the system. We illustrate our approach with some relevant and informative examples.

quant-ph↗

arXiv2023

$\mathcal{C}^{\infty}$-symmetries of distributions and integrability

An extension of the notion of solvable structure for involutive distributions of vector fields is introduced. The new structures are based on a generalization of the concept of symmetry of a distribution of vector fields, inspired in the extension of Lie point symmetries to $\mathcal{C}^{\infty}$-symmetries for ODEs developed in the recent years. These new objects, named $\mathcal{C}^{\infty}$-structures, play a fundamental role in the integrability of the distribution: the knowledge of a $\mathcal{C}^{\infty}$-structure for a corank $k$ involutive distribution permits to find its integral manifolds by solving $k$ successive completely integrable Pfaffian equations. These results have important consequences for the integrability of differential equations. In particular, we derive a new procedure to integrate an $m$th-order ordinary differential equation by splitting the problem into $m$ completely integrable Pfaffian equations. This step-by-step integration procedure is applied to integrate completely several equations that cannot be solved by standard procedures.

nlin.SI↗

arXiv2023

$\mathcal{C}^{\infty}$-structures in the integration of involutive distributions

For a system of ordinary differential equations (ODEs) or, more generally, an involutive distribution of vector fields, the problem of its integration is considered. Among the many approaches to this problem, solvable structures provide a systematic procedure of integration via Pfaffian equations that are integrable by quadratures. In this paper structures more general than solvable structures (named cinf-structures) are considered. The symmetry condition in the concept of solvable structure is weakened for cinf-structures by requiring their vector fields be just cinf-symmetries. For cinf-structures there is also an integration procedure, but the corresponding Pfaffian equations, although completely integrable, are not necessarily integrable by quadratures. The well-known result on the relationship between integrating factors and Lie point symmetries for first-order ODEs is generalized for cinf-structures and involutive distributions of arbitrary corank by introducing symmetrizing factors. The role of these symmetrizing factors on the integrability by quadratures of the Pfaffian equations associated with the \cinf-structure is also established. Some examples that show how these objects and results can be applied in practice are also presented.

math.CA↗

arXiv2021

Truncated Wigner approximation as a non-positive Kraus map

We show that the Truncated Wigner Approximation developed in the flat phase-space is mapped into a Lindblad-type evolution with an indefinite metric in the space of linear operators. As a result, the classically evolved Wigner function corresponds to a non-positive operator $\hat{R}(t)$, which does not describe a physical state. The rate of appearance of negative eigenvalues of $\hat{R}(t)$ can be efficiently estimated. The short-time dynamics of the Kerr and second harmonic generation Hamiltonains are discussed.

quant-ph↗

arXiv2016

Correlation transfer in large-spin chains

It is shown that transient spin-spin correlations in one-dimensional spin S>>1 chain can be enhanced for initially factorized and individually squeezed spin states. Such correlation transfer form "internal" to "external" degrees of freedom can be well described by using a semiclassical phase-space approach.

quant-ph↗

arXiv2016

$λ-$Symmetries and integrability by quadratures

It is investigated how two (standard or generalized) $λ-$symmetries of a given second-order ordinary differential equation can be used to solve the equation by quadratures. The method is based on the construction of two commuting generalized symmetries for this equation by using both $λ-$symmetries. The functions used in that construction are related with integrating factors of the reduced and auxiliary equations associated to the $λ-$symmetries. These functions can also be used to derive a Jacobi last multiplier and two integrating factors for the given equation. Some examples illustrate the method; one of them is included in the XXVII case of the Painlevé-Gambier classification. An explicit expression of its general solution in terms of two fundamental sets of solutions for two related second-order linear equations is also obtained.

math.CA↗

arXiv2008

Discrete phase-space structure of $n$-qubit mutually unbiased bases

We work out the phase-space structure for a system of $n$ qubits. We replace the field of real numbers that label the axes of the continuous phase space by the finite field $\Gal{2^n}$ and investigate the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties. We provide a simple classification of such curves and study in detail the four- and eight-dimensional cases, analyzing also the effect of local transformations. In this way, we provide a comprehensive phase-space approach to the construction of mutually unbiased bases for $n$ qubits.

quant-ph↗

arXiv2007

Quantum light depolarization: the phase-space perspective

Quantum light depolarization is handled through a master equation obtained by coupling dispersively the field to a randomly distributed atomic reservoir. This master equation is solved by transforming it into a quasiprobability distribution in phase space and the quasiclassical limit is investigated.

quant-ph↗

arXiv2007

Geometrical approach to mutually unbiased bases

We propose a unifying phase-space approach to the construction of mutually unbiased bases for a two-qubit system. It is based on an explicit classification of the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties. We also consider the feasible transformations between different kinds of curves and show that they correspond to local rotations around the Bloch-sphere principal axes. We suggest how to generalize the method to systems in dimensions that are powers of a prime.

quant-ph↗

arXiv2006

Geometric approach to the discrete Wigner function

We analyze the Wigner function constructed on the basis of the discrete rotation and displacement operators labeled with elements of the underlying finite field. We separately discuss the case of odd and even characteristics and analyze the algebraic origin of the non uniqueness of the representation of the Wigner function. Explicit expressions for the Wigner kernel are given in both cases.

quant-ph↗

arXiv2005

Simple quantum model for light depolarization

Depolarization of quantum fields is handled through a master equation of the Lindblad type. The specific feature of the proposed model is that it couples dispersively the field modes to a randomly distributed atomic reservoir, much in the classical spirit of dealing with this problem. The depolarizing dynamics resulting from this model is analyzed for relevant states.

quant-ph↗

arXiv2005

Certainty relations between local and nonlocal observables

We demonstrate that for an arbitrary number of identical particles, each defined on a Hilbert-space of arbitrary dimension, there exists a whole ladder of relations of complementarity between local, and every conceivable kind of joint (or nonlocal) measurements. E.g., the more accurate we can know (by a measurement) some joint property of three qubits (projecting the state onto a tripartite entangled state), the less accurate some other property, local to the three qubits, become. We also show that the corresponding complementarity relations are particularly tight for particles defined on prime dimensional Hilbert spaces.

quant-ph↗

arXiv2005

On the structure of the sets of mutually unbiased bases for N qubits

For a system of N qubits, spanning a Hilbert space of dimension d=2^N, it is known that there exists d+1 mutually unbiased bases. Different construction algorithms exist, and it is remarkable that different methods lead to sets of bases with different properties as far as separability is concerned. Here we derive the four sets of nine bases for three qubits, and show how they are unitarily related. We also briefly discuss the four-qubit case, give the entanglement structure of sixteen sets of bases,and show some of them, and their interrelations, as examples. The extension of the method to the general case of N qubits is outlined.

quant-ph↗

arXiv2003

Effective damping in the Raman cooling of trapped ions

We present a method of treating the interaction of a single three-level ion with two laser beams. The idea is to apply a unitary transformation such that the exact transformed Hamiltonian has one of the three levels decoupled for all values of the detunings. When one takes into account damping, the evolution of the system is governed by a master equation usually obtained via adiabatic approximation under the assumption of far-detuned lasers. To go around the drawbacks of this technique, we use the same unitary transformation to get an effective master equation.

quant-ph↗

arXiv2003

Near-threshold production of the multi-strange $Ξ^-$ hyperon

The yield for the multi-strange $Ξ^{-}$ hyperon has been measured in 6 AGeV Au+Au collisions via reconstruction of its decay products $π^{-}$ and $Λ$, the latter also being reconstructed from its daughter tracks of $π^{-}$ and p. The measurement is rather close to the threshold for $Ξ^{-}$ production and therefore provides an important test of model predictions. The measured yield for $Ξ^{-}$ and $Λ$ are compared for several centralities. In central collisions the $Ξ^{-}$ yield is found to be in excellent agreement with statistical and transport model predictions, suggesting that multi-strange hadron production approaches chemical equilibrium in high baryon density nuclear matter.

nucl-ex↗

arXiv2003

Comparison of Source Images for protons, $π^-$'s and $Λ$'s in 6 AGeV Au+Au collisions

Source images are extracted from two-particle correlations constructed from strange and non-strange hadrons produced in 6 AGeV Au + Au collisions. Very different source images result from pp vs p$Λ$ vs $π^-π^-$ correlations. These observations suggest important differences in the space-time emission histories for protons, pions and neutral strange baryons produced in the same events.

nucl-ex↗

arXiv2002

The Forward Time Projection Chamber (FTPC) in STAR

Two cylindrical forward TPC detectors are described which were constructed to extend the phase space coverage of the STAR experiment to the region 2.5 < |η| < 4.0. For optimal use of the available space and in order to cope with the high track density of central Au+Au collisions at RHIC, a novel design was developed using radial drift in a low diffusion gas. From prototype measurements a 2-track resolution of 1-2 mm is expected.

nucl-ex↗