Practical implementation of mutually unbiased bases using quantum circuits

The number of measurements necessary to perform the quantum state reconstruction of a system of qubits grows exponentially with the number of constituents, creating a major obstacle for the design of scalable tomographic schemes. We work out a simple and efficient method based on cyclic generation of mutually unbiased bases. The basic generator requires only Hadamard and controlled-phase gates, which are available in most practical realizations of these systems. We show how complete sets of mutually unbiased bases with different entanglement structures can be realized for three and four qubits. We also analyze the quantum circuits implementing the various entanglement classes.Comment: 5 pages, 2 color figures. Comments welcome

Discrete phase-space structure of nn-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.Comment: Title changed. Improved version. Accepted for publication in Annals of Physic

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.Comment: 16 pages, 5 figure

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.Comment: To appear in Phys. Rev.

Renormalization Group and Grand Unification with 331 Models

By making a renormalization group analysis we explore the possibility of having a 331 model as the only intermediate gauge group between the standard model and the scale of unification of the three coupling constants. We shall assume that there is no necessarily a group of grand unification at the scale of convergence of the couplings. With this scenario, different 331 models and their corresponding supersymmetric versions are considered, and we find the versions that allow the symmetry breaking described above. Besides, the allowed interval for the 331 symmetry breaking scale, and the behavior of the running coupling constants are obtained. It worths saying that some of the supersymmetric scenarios could be natural frameworks for split supersymmetry. Finally, we look for possible 331 models with a simple group at the grand unification scale, that could fit the symmetry breaking scheme described above.Comment: 18 pages. 3 figures. Some results reinterpreted, a new section and references added. Version to appear in International Journal of Modern Physics

Unpolarized states and hidden polarization

We capitalize on a multipolar expansion of the polarisation density matrix, in which multipoles appear as successive moments of the Stokes variables. When all the multipoles up to a given order $K$ vanish, we can properly say that the state is $K$th-order unpolarized, as it lacks of polarization information to that order. First-order unpolarized states coincide with the corresponding classical ones, whereas unpolarized to any order tally with the quantum notion of fully invariant states. In between these two extreme cases, there is a rich variety of situations that are explored here. The existence of \textit{hidden} polarisation emerges in a natural way in this context.Comment: 7 pages, 3 eps-color figures. Submitted to PRA. Comments welcome

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 multilayers occurs. By resorting to the notion of area under the transmittance curve, we assess in a systematic way the performance of the different quasiperiodic Fibonacci multilayers.Comment: 5 pages, 4 color figures. Comments welcome