Distances between quantum states in the tomographic-probability representation

Distances between quantum states are reviewed within the framework of the tomographic-probability representation. Tomographic approach is based on observed probabilities and is straightforward for data processing. Different states are distinguished by comparing corresponding probability-distribution functions. Fidelity as well as other distance measures are expressed in terms of tomograms.Comment: 10 pages, Contribution to the 16th Central European Workshop on Quantum Optics (CEWQO'09), May 23-27, 2009, Turku, Finlan

Derivative pricing under the possibility of long memory in the supOU stochastic volatility model

We consider the supOU stochastic volatility model which is able to exhibit long-range dependence. For this model we give conditions for the discounted stock price to be a martingale, calculate the characteristic function, give a strip where it is analytic and discuss the use of Fourier pricing techniques. Finally, we present a concrete specification with polynomially decaying autocorrelations and calibrate it to observed market prices of plain vanilla options

Bargmann-Michel-Telegdi equation and one-particle relativistic approach

A reexamination of the semiclassical approach of the relativistic electron indicates a possible variation of its helicity for electric and magnetic static fields applied along its global motion due to zitterbewegung effects, proportional to the anomalous part of the magnetic moment.Comment: 10 pages, LATEX2E, uses amsb

Rabi oscillations in the four-level double-dot structure under the influence of the resonant pulse

We study theoretically the quantum dynamics of an electron in the symmetric four-level double-dot structure under the influence of the monochromatic resonant pulse. The probability amplitudes of the eigenstates relevant for the quantum dynamics are found from the solution of the non-stationary Schr\"odinger equation. The first-order correction term to the solution obtained through the rotating wave approximation is calculated. The three-level double-dot dynamics and the two-level single-dot dynamics, as well as the off-resonant excitation process, are derived from the general formulae for corresponding choices of the pulse and structure parameters. The results obtained may be applied to the solid-state qubit design.Comment: Accepted for publication in Phys. Rev.

Classical bifurcations and entanglement in smooth Hamiltonian system

We study entanglement in two coupled quartic oscillators. It is shown that the entanglement, as measured by the von Neumann entropy, increases with the classical chaos parameter for generic chaotic eigenstates. We consider certain isolated periodic orbits whose bifurcation sequence affects a class of quantum eigenstates, called the channel localized states. For these states, the entanglement is a local minima in the vicinity of a pitchfork bifurcation but is a local maxima near a anti-pitchfork bifurcation. We place these results in the context of the close connections that may exist between entanglement measures and conventional measures of localization that have been much studied in quantum chaos and elsewhere. We also point to an interesting near-degeneracy that arises in the spectrum of reduced density matrices of certain states as an interplay of localization and symmetry.Comment: 7 pages, 6 figure

Computation by measurements: a unifying picture

The ability to perform a universal set of quantum operations based solely on static resources and measurements presents us with a strikingly novel viewpoint for thinking about quantum computation and its powers. We consider the two major models for doing quantum computation by measurements that have hitherto appeared in the literature and show that they are conceptually closely related by demonstrating a systematic local mapping between them. This way we effectively unify the two models, showing that they make use of interchangeable primitives. With the tools developed for this mapping, we then construct more resource-effective methods for performing computation within both models and propose schemes for the construction of arbitrary graph states employing two-qubit measurements alone.Comment: 13 pages, 18 figures, REVTeX

Optimal estimation of one parameter quantum channels

We explore the task of optimal quantum channel identification, and in particular the estimation of a general one parameter quantum process. We derive new characterizations of optimality and apply the results to several examples including the qubit depolarizing channel and the harmonic oscillator damping channel. We also discuss the geometry of the problem and illustrate the usefulness of using entanglement in process estimation.Comment: 23 pages, 4 figures. Published versio

Shear Flow Generation and Energetics in Electromagnetic Turbulence

Zonal flows are recognised to play a crucial role for magnetised plasma confinement. The genesis of these flows out of turbulent fluctuations is therefore of significant interest. We investigate the relative importance of zonal flow generation mechanisms via the Reynolds stress, Maxwell stress, and geodesic acoustic mode (GAM) transfer in drift-Alfv\'en turbulence. By means of numerical computations we quantify the energy transfer into zonal flows owing to each of these effects. The importance of the three driving ingredients in electrostatic and electromagnetic turbulence for conditions relevant to the edge of fusion devices is revealed for a broad range of parameters. The Reynolds stress is found to provide a flow drive, while the electromagnetic Maxwell stress is in the cases considered a sink for the flow energy. In the limit of high plasma beta, where electromagnetic effects and Alfv\'en dynamics are important, the Maxwell stress is found to cancel the Reynolds stress to a high degree. The geodesic oscillations, related to equilibrium pressure profile modifications due to poloidally asymmetric transport, can act as both sinks as drive terms, depending on the parameter regime. For high beta cases the GAMs are the main drive of the flow. This is also reflected in the frequency dependence of the flow, showing a distinct peak at the GAM frequency in that regime.Comment: 16 pages, 12 Figure

Generation of decoherence-free displaced squeezed states of radiation fields and a squeezed reservoir for atoms in cavity QED

We present a way to engineer an effective anti-Jaynes-Cumming and a Jaynes-Cumming interaction between an atomic system and a single cavity mode and show how to employ it in reservoir engineering processes. To construct the effective Hamiltonian, we analyse considered the interaction of an atomic system in a \{Lambda} configuration, driven by classical fields, with a single cavity mode. With this interaction, we firstly show how to generate a decoherence-free displaced squeezed state for the cavity field. In our scheme, an atomic beam works as a reservoir for the radiation field trapped inside the cavity, as employed recently by S. Pielawa et al. [Phys. Rev. Lett. 98, 240401 (2007)] to generate an Einstein-Podolsky-Rosen entangled radiation state in high-Q resonators. In our scheme, all the atoms have to be prepared in the ground state and, as in the cited article, neither atomic detection nor precise interaction times between the atoms and the cavity mode are required. From this same interaction, we can also generate an ideal squeezed reservoir for atomic systems. For this purpose we have to assume, besides the engineered atom-field interaction, a strong decay of the cavity field (i.e., the cavity decay must be much stronger than the effective atom-field coupling). With this scheme, some interesting effects in the dynamics of an atom in a squeezed reservoir could be tested