L. L. Sanchez-Soto

Entangled-State Lithography: Tailoring Any Pattern with a Single State

We demonstrate a systematic approach to Heisenberg-limited lithographic image formation using four-mode reciprocal binomial states. By controlling the exposure pattern with a simple bank of birefringent plates, any pixel pattern on a (N+1) x (N+1) grid, occupying a square with the side half a wavelength long, can be generated from a 2N-photon state.

Structure of the sets of mutually unbiased bases for N qubits

For a system of N qubits, living in a Hilbert space of dimension d=2{sup 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 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 16 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.

Comparing omnidirectional reflection from periodic and quasiperiodic one-dimensional photonic crystals.

We determine the range of thicknesses and refractive indices for which omnidirectional reflection from quasiperiodic dielectric multilayers occurs. By resorting to the notion of area under the transmittance curve, we assess in a systematic way the performance of the different Fibonacci multilayers.

Wavefront sensing reveals optical coherence

Wavefront sensing is a set of techniques providing efficient means to ascertain the shape of an optical wavefront or its deviation from an ideal reference. Owing to its wide dynamical range and high optical efficiency, the Shack-Hartmann wavefront sensor is nowadays the most widely used of these sensors. Here we show that it actually performs a simultaneous measurement of position and angular spectrum of the incident radiation and, therefore, when combined with tomographic techniques previously developed for quantum information processing, the Shack-Hartmann wavefront sensor can be instrumental in reconstructing the complete coherence properties of the signal. We confirm these predictions with an experimental characterization of partially coherent vortex beams, a case that cannot be treated with the standard tools. This seems to indicate that classical methods employed hitherto do not fully exploit the potential of the registered data.

The transfer matrix: A geometrical perspective

Abstract 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 a b c d 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.

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.

Radial quantum number of Laguerre-Gauss modes

(Received 31 January 2014; published 16 June 2014)We introduce an operator linked with the radial index in the Laguerre-Gauss modes of a two-dimensionalharmonicoscillatorincylindricalcoordinates.Wediscussladderoperatorsforthisvariable,andconfirmthattheyobey the commutation relations of the su(1,1) algebra. Using this fact, we examine how basic quantum opticalconcepts can be recast in terms of radial modes.DOI: 10.1103/PhysRevA.89.063813 PACS number(s): 42

Lossless multilayers and Lorentz transformations: more than an analogy

It is shown that the matrix describing a lossless multilayer when no total reflection occurs is an element of the group SU(1,1), which is locally isomorphic to the three-dimensional Lorentz group SO(2,1). A natural identification of the reflection and transmission coefficients for the multilayer with the parameters of a Lorentz transformation is performed. The correspondence between field and space-time variables, along with the invariance of the interval, allows us to compute the invariant of the multilayer.

The discrete Wigner function

Publisher Summary Until quite recently, Wigner functions were used mostly for infinite-dimensional Hilbert spaces. However, many quantum systems can be appropriately described in a finite-dimensional Hilbert space. These include, among other, spin systems, multi-level atoms, optical fields with a fixed number of photons, and electrons occupying a finite number of sites. When considering the coherent superpositions of ‘classical’ states, the discrete Wigner function behaves in a way that differs drastically from its continuous counterpart: the interference spreads over all of phase space, affecting even the regions where the original states are localized. As a consequence, the presence of interference may become hard to identify when using this class of Wigner functions. However, given two orthogonal stabilizer ‘classical’ states it is possible to define a Wigner function such that all coherent super-positions of those states have a phase-space representation in which the quantum interference is localized. This chapter discusses the continuous Wigner function, followed by discrete finite space and finite fields. It also discusses the generalized Pauli group, mutually unbiased bases, and the discrete Wigner function. This is followed by a discussion on reconstruction of the density operator from the discrete Wigner function, its applications.

Quantum phases of a qutrit

We consider various approaches to treat the phases of a qutrit. Although it is possible to represent qutrits in a convenient geometrical manner by resorting to a generalization of the Poincare sphere, we argue that the appropriate way of dealing with this problem is through phase operators associated with the algebra su(3). The rather unusual properties of these phases are caused by the small dimension of the system and are explored in detail. We also examine the positive operator-valued measures that can describe the qutrit phase properties.