Discrete Wigner functions and the phase space representation of quantum teleportation

We present a phase space description of the process of quantum teleportation for a system with an $N$ dimensional space of states. For this purpose we define a discrete Wigner function which is a minor variation of previously existing ones. This function is useful to represent composite quantum system in phase space and to analyze situations where entanglement between subsystems is relevant (dimensionality of the space of states of each subsystem is arbitrary). We also describe how a direct tomographic measurement of this Wigner function can be performed.Comment: 8 pages, 1 figure, to appear in Phys Rev

Statistics of dressed modes in a thermal state

By a Wigner-function calculation, we evaluate the trace of a certain Gaussian operator arising in the theory of a boson system subject to both finite temperature and (weak) interaction. Thereby we rederive (and generalize) a recent result by Kocharovsky, Kocharovsky, and Scully [Phys. Rev. A, vol. 61, art. 053606 (2000)] in a way that is technically much simpler. One step uses a special case of the response of Wigner functions to linear transformations, and we demonstrate the general case by simple means. As an application we extract the counting statistics for each mode of the Bose gas.Comment: to appear in Optics Communications, 10 page

Comparison of different procedures to map reference evapotranspiration using geographical information systems and regression-based techniques

16 páginas, 6 figuras, 8 tablas.This paper compares different procedures for mapping reference evapotranspiration (ETo) by means of regression-based techniques and geographical information systems (GIS). ETo is calculated following the method of Hargreaves (HG) from a dense database of meteorological stations in the northernmost semi-arid region of Europe, the Ebro valley. The HG method requires the calculation of estimates of extraterrestrial radiation (Ra). We calculated this parameter using two approaches: (1) the common approach that assumes a planar surface and determines the parameter as a function of latitude and (2) using a digital terrain model (DTM) and GIS modelling. The maps were made on a monthly basis using both approaches. We also compared possible propagations of errors in the map calculations for maps derived from modelled layers of maximum and minimum temperatures with those modelled using previously determined local ETo calculations. We demonstrate that calculations of Ra from a DTM and GIS modelling provide a more realistic spatial distribution of ETo than those derived by only considering latitude. It is also preferable to model in advance the variables involved in the calculation of ETo (temperature and Ra) and to subsequently calculate ETo by means of layer algebra in the GIS rather than directly model the local ETo calculations. The obtained maps are useful for the purposes of agriculture and ecological and water resources management in the study area.This work has been supported by the project CGL2005- 04508/BOS financed by the Spanish Comission of Science and Technology (CICYT) and FEDER, PIP176/2005 financed by the Aragón Government, and ‘Programa de grupos de investigación consolidados’ (BOA 48 of 20-04-2005), also financed by the Aragón Government. Research of the third author was supported by postdoctoral fellowship by the Ministerio de Educación, Cultura y Deporte (Spain).Peer reviewe

Quantum properties of the codirectional three-mode Kerr nonlinear coupler

We investigate the quantum properties for the codirectional three-mode Kerr nonlinear coupler. We investigate single-, two- and three-mode quadrature squeezing, Wigner function and purity. We prove that this device can provide richer nonclassical effects than those produced by the conventional coupler, i.e. the two-mode Kerr coupler. We show that it can provide squeezing and the quadrature squeezing exhibiting leaf-revival-collapse phenomenon in dependence on the values of the interaction parameters. In contrast to the conventional Kerr coupler two different forms of cat states can be simultaneously generated in the waveguides. We deduce conditions required for the complete disentanglement between the components of the system.Comment: 23 pages, 6 figure

Quantum-circuit guide to optical and atomic interferometry

Atomic (qubit) and optical or microwave (modal) phase-estimation protocols are placed on the same footing in terms of quantum-circuit diagrams. Circuit equivalences are used to demonstrate the equivalence of protocols that achieve the Heisenberg limit by employing entangled superpositions of Fock states, such as N00N states. The key equivalences are those that disentangle a circuit so that phase information is written exclusively on a mode or modes or on a qubit. The Fock-state-superposition phase-estimation circuits are converted to use entangled coherent-state superpositions; the resulting protocols are more amenable to realization in the lab, particularly in a qubit/cavity setting at microwave frequencies.Comment: To appear in Optics Communications special issue in memory of Krzysztof Wodkiewic

Sampling functions for multimode homodyne tomography with a single local oscillator

We derive various sampling functions for multimode homodyne tomography with a single local oscillator. These functions allow us to sample multimode s-parametrized quasidistributions, density matrix elements in Fock basis, and s-ordered moments of arbitrary order directly from the measured quadrature statistics. The inevitable experimental losses can be compensated by proper modification of the sampling functions. Results of Monte Carlo simulations for squeezed three-mode state are reported and the feasibility of reconstruction of the three-mode Q-function and s-ordered moments from 10^7 sampled data is demonstrated.Comment: 12 pages, 8 figures, REVTeX, submitted Phys. Rev.

Quantum computers in phase space

We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples, such as the Fourier Transform and Grover's search, we examine the conditions for the existence of a direct correspondence between quantum and classical evolutions in phase space. Finally, we describe how to directly measure the Wigner function in a given phase space point by means of a tomographic method that, itself, can be interpreted as a simple quantum algorithm.Comment: 16 pages, 7 figures, to appear in Phys Rev

Quantum phase gate with a selective interaction

We present a proposal for implementing quantum phase gates using selective interactions. We analize selectivity and the possibility to implement these gates in two particular systems, namely, trapped ions and Cavity QED.Comment: Four pages of TEX file and two EPS figures. Submitted for publicatio

Recovering coherence from decoherence: a method of quantum state reconstruction

We present a feasible scheme for reconstructing the quantum state of a field prepared inside a lossy cavity. Quantum coherences are normally destroyed by dissipation, but we show that at zero temperature we are able to retrieve enough information about the initial state, making possible to recover its Wigner function as well as other quasiprobabilities. We provide a numerical simulation of a Schroedinger cat state reconstruction.Comment: 8 pages, in RevTeX, 4 figures, accepted for publication in Phys. Rev. A (november 1999