Complex chaos in conditional qubit dynamics and purification protocols

Selection of an ensemble of equally prepared quantum systems, based on measurements on it, is a basic step in quantum state purification. For an ensemble of single qubits, iterative application of selective dynamics has been shown to lead to complex chaos, which is a novel form of quantum chaos with true sensitivity to the initial conditions. The Julia set of initial valuse with no convergence shows a complicated structre on the complex plane. The shape of the Julia set varies with the parameter of the dynamics. We present here results for the two qubit case demonstrating how a purification process can be destroyed with chaotic oscillations

Complex chaos in the conditional dynamics of qubits

We analyze the consequences of iterative measurement-induced nonlinearity on the dynamical behavior of qubits. We present a one-qubit scheme where the equation governing the time evolution is a complex-valued nonlinear map with one complex parameter. In contrast to the usual notion of quantum chaos, exponential sensitivity to the initial state occurs here. We calculate analytically the Lyapunov exponent based on the overlap of quantum states, and find that it is positive. We present a few illustrative examples of the emerging dynamics.Comment: 4 pages, 3 figure

Optimized quantum random-walk search algorithms

Shenvi, Kempe and Whaley's quantum random-walk search (SKW) algorithm [Phys. Rev. A 67, 052307 (2003)] is known to require $O(\sqrt N)$ number of oracle queries to find the marked element, where $N$ is the size of the search space. The overall time complexity of the SKW algorithm differs from the best achievable on a quantum computer only by a constant factor. We present improvements to the SKW algorithm which yield significant increase in success probability, and an improvement on query complexity such that the theoretical limit of a search algorithm succeeding with probability close to one is reached. We point out which improvement can be applied if there is more than one marked element to find.Comment: 7 pages, 2 figures. Major revision according to referee repor

Scattering quantum random-walk search with errors

We analyze the realization of a quantum-walk search algorithm in a passive, linear optical network. The specific model enables us to consider the effect of realistic sources of noise and losses on the search efficiency. Photon loss uniform in all directions is shown to lead to the rescaling of search time. Deviation from directional uniformity leads to the enhancement of the search efficiency compared to uniform loss with the same average. In certain cases even increasing loss in some of the directions can improve search efficiency. We show that while we approach the classical limit of the general search algorithm by introducing random phase fluctuations, its utility for searching is lost. Using numerical methods, we found that for static phase errors the averaged search efficiency displays a damped oscillatory behaviour that asymptotically tends to a non-zero value.Comment: 10 pages, 10 figures. Two figures added for clarity, also made improvements to the tex

Directional correlations in quantum walks with two particles

Quantum walks on a line with a single particle possess a classical analogue. Involving more walkers opens up the possibility of studying collective quantum effects, such as many-particle correlations. In this context, entangled initial states and the indistinguishability of the particles play a role. We consider the directional correlations between two particles performing a quantum walk on a line. For non-interacting particles, we find analytic asymptotic expressions and give the limits of directional correlations. We show that by introducing delta-interaction between the particles, one can exceed the limits for non-interacting particles

Discovery of the spectroscopic binary nature of six southern Cepheids

We present the analysis of photometric and spectroscopic data of six bright Galactic Cepheids: GH Carinae, V419 Centauri, V898 Centauri, AD Puppis, AY Sagittarii, and ST Velorum. Based on new radial velocity data (in some cases supplemented with earlier data available in the literature), these Cepheids have been found to be members in spectroscopic binary systems. V898 Cen turned out to have one of the largest orbital radial velocity amplitude (> 40 km/s) among the known binary Cepheids. The data are insufficient to determine the orbital periods nor other orbital elements for these new spectroscopic binaries. These discoveries corroborate the statement on the high frequency of occurrence of binaries among the classical Cepheids, a fact to be taken into account when calibrating the period-luminosity relationship for Cepheids. We have also compiled all available photometric data that revealed that the pulsation period of AD Pup, the longest period Cepheid in this sample, is continuously increasing with Delta P = 0.004567 d/century, likely to be caused by stellar evolution. The wave-like pattern superimposed on the parabolic O-C graph of AD Pup may well be caused by the light-time effect in the binary system. ST Vel also pulsates with a continuously increasing period. The other four Cepheids are characterised with stable pulsation periods in the last half century.Comment: accepted by the MNRAS, 11 pages, 16 figures, 18 tables, a part of the data can be downloaded from the online version of this articl