arXiv subjects

L. L. Sanchez-Soto

Publications and source records attributed to L. L. Sanchez-Soto.

At least 73 records · Page 4Linked to original sources

arXiv2013

Orbital angular momentum from marginals of quadrature distributions

We set forth a method to analyze the orbital angular momentum of a light field. Instead of using the canonical formalism for the conjugate pair angle-angular momentum, we model this latter variable by the superposition of two independent harmonic oscillators along two orthogonal axes. By describing each oscillator by a standard Wigner function, we derive, via a consistent change of variables, a comprehensive picture of the orbital angular momentum. We compare with previous approaches and show how this method works in some relevant examples.

quant-ph↗

arXiv2013

Sizing up entanglement in mutually unbiased bases with Fisher information

An efficient method for assessing the quality of quantum state tomography is developed. Special attention is paid to the tomography of multipartite systems in terms of unbiased measurements. Although the overall reconstruction errors of different sets of mutually unbiased bases are the same, differences appear when particular aspects of the measured system are contemplated. This point is illustrated by estimating the fidelities of genuinely tripartite entangled states.

quant-ph↗

arXiv2013

Quantum versus classical polarization states: when multipoles count

We advocate for a simple multipole expansion of the polarization density matrix. The resulting multipoles are used to construct bona fide quasiprobability distributions that appear as a sum of successive moments of the Stokes variables; the first one corresponding to the classical picture on the Poincare sphere. We employ the particular case of the $Q$ function to formulate a whole hierarchy of measures that properly assess higher-order polarization correlations.

quant-ph↗

arXiv2013

Nonlinear cross-Kerr quasiclassical dynamics

We study the quasiclassical dynamics of the cross-Kerr effect. In this approximation, the typical periodical revivals of the decorrelation between the two polarization modes disappear and they remain entangled. By mapping the dynamics onto the Poincare space, we find simple conditions for polarization squeezing. When dissipation is taken into account, the shape of the states in such a space is not considerably modified, but their size is reduced.

quant-ph↗

arXiv2013

Optimal quantum tomography of permutationally invariant qubits

Mutually unbiased bases determine an optimal set of measurements to extract complete information about the quantum state of a system. However, quite often a priori information about the state exist, making some of the measurement bases superfluous. This is, for example, the case when multiqubit states belong to the permutationally invariant subspace. In this paper we derive the minimal sets of mutually unbiased bases needed to tomographically reconstruct such states.

quant-ph↗

arXiv2012

Informational completeness of continuous-variable measurements

We justify that homodyne tomography turns out to be informationally complete when the number of independent quadrature measurements is equal to the dimension of the density matrix in the Fock representation. Using this as our thread, we examine the completeness of other schemes, when continuous-variable observations are truncated to discrete finite-dimensional subspaces.

quant-ph↗

arXiv2012

Complementarity and phases in SU(3)

Phase operators and phase states are introduced for irreducible representations of the Lie algebra su(3) using a polar decomposition of ladder operators. In contradistinction with su(2), it is found that the su(3) polar decomposition does not uniquely determine a Hermitian phase operator. We describe two possible ways of proceeding: one based in imposing SU(2) invariance and the other based on the idea of complementarity. The generalization of these results to SU(n) is sketched.

math-ph↗

arXiv2012

Symmetric discrete coherent states for n qubits

We put forward a method of constructing discrete coherent states for n qubits. After establishing appropriate displacement operators, the coherent states appear as displaced versions of a fiducial vector that is fixed by imposing a number of natural symmetry requirements on its Q-function. Using these coherent states we establish a partial order in the discrete phase space, which allows us to picture some n-qubit states as apparent distributions. We also analyze correlations in terms of sums of squared Q-functions.

quant-ph↗

arXiv2012

Graph states in phase space

The phase space for a system of $n$ qubits is a discrete grid of $2^{n} \times 2^{n}$ points, whose axes are labeled in terms of the elements of the finite field $\Gal{2^n}$ to endow it with proper geometrical properties. We analyze the representation of graph states in that phase space, showing that these states can be identified with a class of non-singular curves. We provide an algebraic representation of the most relevant quantum operations acting on these states and discuss the advantages of this approach.

quant-ph↗

arXiv2012

The transfer matrix: a geometrical perspective

We present a comprehensive and self-contained discussion of the use of the transfer matrix to study propagation in one-dimensional lossless systems, including a variety of examples, such as superlattices, photonic crystals, and optical resonators. In all these cases, the transfer matrix has the same algebraic properties as the Lorentz group in a (2+1)-dimensional spacetime, as well as the group of unimodular real matrices underlying the structure of the abcd law, which explains many subtle details. We elaborate on the geometrical interpretation of the transfer-matrix action as a mapping on the unit disk and apply a simple trace criterion to classify the systems into three types with very different geometrical and physical properties. This approach is applied to some practical examples and, in particular, an alternative framework to deal with periodic (and quasiperiodic) systems is proposed.

cond-mat.stat-mech↗

arXiv2012

Quantum polarization tomography of bright squeezed light

We reconstruct the polarization sector of a bright polarization squeezed beam starting from a complete set of Stokes measurements. Given the symmetry that underlies the polarization structure of quantum fields, we use the unique SU(2) Wigner distribution to represent states. In the limit of localized and bright states, the Wigner function can be approximated by an inverse three-dimensional Radon transform. We compare this direct reconstruction with the results of a maximum likelihood estimation, finding an excellent agreement.

quant-ph↗

arXiv2010

Orbital angular momentum in phase space

A comprehensive theory of the Weyl-Wigner formalism for the canonical pair angle-angular momentum is presented. Special attention is paid to the problems linked to rotational periodicity and angular-momentum discreteness.

quant-ph↗

arXiv2010

Quantum degrees of polarization

We discuss different proposals for the degree of polarization of quantum fields. The simplest approach, namely making a direct analogy with the classical description via the Stokes operators, is known to produce unsatisfactory results. Still, we argue that these operators and their properties should be basic for any measure of polarization. We compare alternative quantum degrees and put forth that they order various states differently. This is to be expected, since, despite being rooted in the Stokes operators, each of these measures only captures certain characteristics. Therefore, it is likely that several quantum degrees of polarization will coexist, each one having its specific domain of usefulness.

quant-ph↗

arXiv2010

Robust stationary entanglement of two coupled qubits in independent environments

The dissipative dynamics of two interacting qubits coupled to independent reservoirs at nonzero temperatures is investigated, paying special attention to the entanglement evolution. The counter-rotating terms in the qubit-qubit interaction give rise to stationary entanglement, traceable back to the ground state structure. The robustness of this entanglement against thermal noise is thoroughly analyzed, establishing that it can be detected at reasonable experimental temperatures. Some effects linked to a possible reservoir asymmetry are brought to light.

quant-ph↗

arXiv2010

Nondiffracting beams for vortex tomography

We propose a reconstruction of vortex beams based on the implementation of quadratic transformations in the orbital angular momentum. The information is encoded in a superposition of Bessel-like nondiffracting beams. The measurement of the angular probability distribution at different positions allows for the reconstruction of the Wigner function.

physics.optics↗

arXiv2010

The quantum vacuum at the foundations of classical electrodynamics

In the classical theory of electromagnetism, the permittivity and the permeability of free space are constants whose magnitudes do not seem to possess any deeper physical meaning. By replacing the free space of classical physics with the quantum notion of the vacuum, we speculate that the values of the aforementioned constants could arise from the polarization and magnetization of virtual pairs in vacuum. A classical dispersion model with parameters determined by quantum and particle physics is employed to estimate their values. We find the correct orders of magnitude. Additionally, our simple assumptions yield an independent estimate for the number of charged elementary particles based on the known values of the permittivity and the permeability, and for the volume of a virtual pair. Such interpretation would provide an intriguing connection between the celebrated theory of classical electromagnetism and the quantum theory in the weak field limit.

quant-ph↗

arXiv2010

Assessing the Polarization of a Quantum Field from Stokes Fluctuation

We propose an operational degree of polarization in terms of the variance of the projected Stokes vector minimized over all the directions of the Poincaré sphere. We examine the properties of this degree and show that some problems associated with the standard definition are avoided. The new degree of polarization is experimentally determined using two examples: a bright squeezed state and a quadrature squeezed vacuum.

quant-ph↗

arXiv2009

Angular performance measure for tighter uncertainty relations

The uncertainty principle places a fundamental limit on the accuracy with which we can measure conjugate physical quantities. However, the fluctuations of these variables can be assessed in terms of different estimators. We propose a new angular performance that allows for tighter uncertainty relations for angle and angular momentum. The differences with previous bounds can be significant for particular states and indeed may be amenable to experimental measurement with the present technology.

quant-ph↗