714 research outputs found
An observable measure of entanglement for pure states of multi-qubit systems
Recently, Meyer and Wallach [D.A. Meyer and N.R. Wallach (2002), J. of Math.
Phys., 43, pp. 4273] proposed a measure of multi-qubit entanglement that is a
function on pure states. We find that this function can be interpreted as a
physical quantity related to the average purity of the constituent qubits and
show how it can be observed in an efficient manner without the need for full
quantum state tomography. A possible realization is described for measuring the
entanglement of a chain of atomic qubits trapped in a 3D optical lattice.Comment: 8 pages, 2 figure
Why should anyone care about computing with anyons?
In this article we present a pedagogical introduction of the main ideas and
recent advances in the area of topological quantum computation. We give an
overview of the concept of anyons and their exotic statistics, present various
models that exhibit topological behavior, and we establish their relation to
quantum computation. Possible directions for the physical realization of
topological systems and the detection of anyonic behavior are elaborated.Comment: 22 pages, 13 figures. Some changes to existing sections, several
references added, and a new section on criteria for TQO and TQC in lattice
system
Unsteady, Free Surface Flows; Solutions Employing the Lagrangian Description of the Motion
Numerical techniques for the solution of unsteady free surface flows are briefly reviewed and consideration is given to the feasibility of methods involving parametric planes where the position and shape of the free surface are known in advance. A method for inviscid flows which uses the Lagrangian description of the motion is developed. This exploits the flexibility in the choice of Lagrangian reference coordinates and is readily adapted to include terms due to inhomogeneity of the fluid. Numerical results are compared in two cases of irrotational flow of a homogeneous fluid for which Lagrangian linearized solutions can be constructed. Some examples of wave run-up on a beach and a shelf are then computed
Stability of global entanglement in thermal states of spin chains
We investigate the entanglement properties of a one dimensional chain of spin
qubits coupled via nearest neighbor interactions. The entanglement measure used
is the n-concurrence, which is distinct from other measures on spin chains such
as bipartite entanglement in that it can quantify "global" entanglement across
the spin chain. Specifically, it computes the overlap of a quantum state with
its time-reversed state. As such this measure is well suited to study ground
states of spin chain Hamiltonians that are intrinsically time reversal
symmetric. We study the robustness of n-concurrence of ground states when the
interaction is subject to a time reversal antisymmetric magnetic field
perturbation. The n-concurrence in the ground state of the isotropic XX model
is computed and it is shown that there is a critical magnetic field strength at
which the entanglement experiences a jump discontinuity from the maximum value
to zero. The n-concurrence for thermal mixed states is derived and a threshold
temperature is computed below which the system has non zero entanglement.Comment: 13 pages, 3 figures. v.2 includes minor corrections and an added
section treating the quantum XX model with open boundarie
Some Observations of Flow Patterns and Statistical Properties of Three Component Flows
Vertical air-water flows, solids-water flows and three component air-solids-water flows were investigated in a Three Component Flow Facility. Visual observations of the flow patterns show that three component flows undergo transition and can exhibit strong unsteady vortical motions. Measurements of the fluctuations in cross-sectionally averaged volume fraction measurements were made. The statistical properties of the fluctuations are presented in terms of their amplitude and coherent time scale in the form of the Signal To Noise Ratio (STNR) and the Time Constant (symbol), respectively. Remarkably, the solids-water flows and the dispersed bubbly air-water flows exhibit almost identical values of STNR for the same volume fraction. Equally remarkable in the linear relationship between the Time Constant and the mean bubble or particle velocity; this relationship is found to have the same constant of proportionality for both species in the well behaved disperse regime. In the two-component churn-turbulent and the three-component agitated vortical regimes, the variables (symbol) and STNR significantly deviate from their dispersed regime values. The onset of large coherent structures characteristic of these regimes is reflected by a rise in the amplitude of the fluctuations and a marked increase in their coherent time scale. The results of this study demonstrate the large information content in the fluctuations of the measured quantity, both as a flow regime indicator and as a measure of flow quantities in two- and three-component flows
Measurement of Friction Pressure Drops in Vertical Slurry and Bubbly Flows
A Three Component Flow Facility (TCFF) was used to study friction pressure drops in vertical two component flows of both air bubbles in water and polyester particle-water mixtures. Friction factors of up to two orders in magnitude higher than those at zero volume fraction were observed for both bubbly and slurry flows. This deviation is shown to decrease with increased liquid Reynolds number. Bubbly and slurry flow friction factors were comparably large in magnitude and displayed the same decreasing trend as a function of Reynolds number. The two phase friction multiplier for bubbly flow was shown to attain values up to one order of magnitude higher than the prediction given by Lockhart and Martinelli. Two phase multiplier data is presented for the dispersed flow regime
Some Observations of Flow Patterns and Statistical Properties of Three Component Flows
Air-water flows, solids-water flows and three component air-solids-water flows in a vertical pipe have been investigated in a Three Component Flow Facility. Visual observations of the patterns show that the three component flow exhibits strong unsteady vertical motions which do not occur in the two phase flows studied. Quantitative results of the fluctuating component of the cross-sectionally averaged volume fraction measurements are presented, and related to the nature of the flows. The ratio of the steady component to the r.m.s of the fluctuating component of the volume fraction measurement (Signal To Noise Ratio) is found to be a good flow structure indicator. Remarkably, the solids-water flows and the bubbly air-water flows exhibit almost identical signal to noise ratios for the same volume fraction. However, the corresponding values for the three component flows reflect greater fluctuations corresponding to the vertical structures
Quantum Walks of SU(2)_k Anyons on a Ladder
We study the effects of braiding interactions on single anyon dynamics using
a quantum walk model on a quasi-1-dimensional ladder filled with stationary
anyons. The model includes loss of information of the coin and nonlocal fusion
degrees of freedom on every second time step, such that the entanglement
between the position states and the exponentially growing auxiliary degrees of
freedom is lost. The computational complexity of numerical calculations reduces
drastically from the fully coherent anyonic quantum walk model, allowing for
relatively long simulations for anyons which are spin-1/2 irreps of SU(2)_k
Chern-Simons theory. We find that for Abelian anyons, the walk retains the
ballistic spreading velocity just like particles with trivial braiding
statistics. For non-Abelian anyons, the numerical results indicate that the
spreading velocity is linearly dependent on the number of time steps. By
approximating the Kraus generators of the time evolution map by circulant
matrices, it is shown that the spatial probability distribution for the k=2
walk, corresponding to Ising model anyons, is equal to the classical unbiased
random walk distribution.Comment: 12 pages, 4 figure
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