432 research outputs found
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
Quantum Entangled Dark Solitons Formed by Ultracold Atoms in Optical Lattices
Inspired by experiments on Bose-Einstein condensates in optical lattices, we
study the quantum evolution of dark soliton initial conditions in the context
of the Bose-Hubbard Hamiltonian. An extensive set of quantum measures is
utilized in our analysis, including von Neumann and generalized quantum
entropies, quantum depletion, and the pair correlation function. We find that
quantum effects cause the soliton to fill in. Moreover, soliton-soliton
collisions become inelastic, in strong contrast to the predictions of
mean-field theory. These features show that the lifetime and collision
properties of dark solitons in optical lattices provide clear signals of
quantum effects.Comment: 4 pages, 4 figures; version appearing in PRL, only minor changes from
v
Simulating typical entanglement with many-body Hamiltonian dynamics
We study the time evolution of the amount of entanglement generated by one
dimensional spin-1/2 Ising-type Hamiltonians composed of many-body
interactions. We investigate sets of states randomly selected during the time
evolution generated by several types of time-independent Hamiltonians by
analyzing the distributions of the amount of entanglement of the sets. We
compare such entanglement distributions with that of typical entanglement,
entanglement of a set of states randomly selected from a Hilbert space with
respect to the unitarily invariant measure. We show that the entanglement
distribution obtained by a time-independent Hamiltonian can simulate the
average and standard deviation of the typical entanglement, if the Hamiltonian
contains suitable many-body interactions. We also show that the time required
to achieve such a distribution is polynomial in the system size for certain
types of Hamiltonians.Comment: Revised, 11 pages, 7 figure
Global Entanglement for Multipartite Quantum States
Based on the residual entanglement [9] (Phys. Rev. A \textbf{71}, 044301
(2005)), we present the global entanglement for a multipartite quantum state.
The measure is shown to be also obtained by the bipartite partitions of the
multipartite state. The distinct characteristic of the global entanglement is
that it consists of the sum of different entanglement contributions. The
measure can provide sufficient and necessary condition of fully separability
for pure states and be conveniently extended to mixed states by minimizing the
convex hull. To test the sufficiency of the measure for mixed states, we
evaluate the global entanglement of bound entangled states. The properties of
the measure discussed finally show the global entanglement is an entanglement
monotone.Comment: 6 page
Loops and Strings in a Superconducting Lattice Gauge Simulator
We propose an architecture for an analog quantum simulator of
electromagnetism in 2+1 dimensions, based on an array of superconducting
fluxonium devices. The encoding is in the integer (spin-1 representation of the
quantum link model formulation of compact U(1) lattice gauge theory. We show
how to engineer Gauss' law via an ancilla mediated gadget construction, and how
to tune between the strongly coupled and intermediately coupled regimes. The
witnesses to the existence of the predicted confining phase of the model are
provided by nonlocal order parameters from Wilson loops and disorder parameters
from 't Hooft strings. We show how to construct such operators in this model
and how to measure them nondestructively via dispersive coupling of the
fluxonium islands to a microwave cavity mode. Numerical evidence is found for
the existence of the confined phase in the ground state of the simulation
Hamiltonian on a ladder geometry.Comment: 17 pages, 5 figures. Published versio
Entanglement of localized states
We derive exact expressions for the mean value of Meyer-Wallach entanglement
Q for localized random vectors drawn from various ensembles corresponding to
different physical situations. For vectors localized on a randomly chosen
subset of the basis, tends for large system sizes to a constant which
depends on the participation ratio, whereas for vectors localized on adjacent
basis states it goes to zero as a constant over the number of qubits.
Applications to many-body systems and Anderson localization are discussed.Comment: 6 pages, 4 figure
Probability density function characterization of multipartite entanglement
We propose a method to characterize and quantify multipartite entanglement
for pure states. The method hinges upon the study of the probability density
function of bipartite entanglement and is tested on an ensemble of qubits in a
variety of situations. This characterization is also compared to several
measures of multipartite entanglement.Comment: 7 pages, 2 figures; published version; title changed; further
explanations and comparison with several measures of multipartite
entanglement adde
Momentum-space analysis of multipartite entanglement at quantum phase transitions
We investigate entanglement properties at quantum phase transitions of an
integrable extended Hubbard model in the momentum space representation. Two
elementary subsystems are recognized: the single mode of an electron, and the
pair of modes (electrons coupled through the eta-pairing mechanism). We first
detect the two/multi-partite nature of each quantum phase transition by a
comparative study of the singularities of Von Neumann entropy and quantum
mutual information. We establish the existing relations between the
correlations in the momentum representation and those exhibited in the
complementary picture: the direct lattice representation. The presence of
multipartite entanglement is then investigated in detail through the Q-measure,
namely a generalization of the Meyer-Wallach measure of entanglement. Such a
measure becomes increasingly sensitive to correlations of a multipartite nature
increasing the size of the reduced density matrix. In momentum space, we
succeed in obtaining the latter for our system at arbitrary size and we relate
its behaviour to the nature of the various QPTs.Comment: 8 pages, 4 figure
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