330 research outputs found
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
Intermediate quantum maps for quantum computation
We study quantum maps displaying spectral statistics intermediate between
Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum
computer with a small number of gates, and efficiently yield information about
fidelity decay or spectral statistics. We study their matrix elements and
entanglement production, and show that they converge with time to distributions
which differ from random matrix predictions. A randomized version of these maps
can be implemented even more economically, and yields pseudorandom operators
with original properties, enabling for example to produce fractal random
vectors. These algorithms are within reach of present-day quantum computers.Comment: 4 pages, 4 figures, research done at
http://www.quantware.ups-tlse.fr
How large can the electron to proton mass ratio be in Particle-In-Cell simulations of unstable systems?
Particle-in-cell (PIC) simulations are widely used as a tool to investigate
instabilities that develop between a collisionless plasma and beams of charged
particles. However, even on contemporary supercomputers, it is not always
possible to resolve the ion dynamics in more than one spatial dimension with
such simulations. The ion mass is thus reduced below 1836 electron masses,
which can affect the plasma dynamics during the initial exponential growth
phase of the instability and during the subsequent nonlinear saturation. The
goal of this article is to assess how far the electron to ion mass ratio can be
increased, without changing qualitatively the physics. It is first demonstrated
that there can be no exact similarity law, which balances a change of the mass
ratio with that of another plasma parameter, leaving the physics unchanged.
Restricting then the analysis to the linear phase, a criterion allowing to
define a maximum ratio is explicated in terms of the hierarchy of the linear
unstable modes. The criterion is applied to the case of a relativistic electron
beam crossing an unmagnetized electron-ion plasma.Comment: To appear in Physics of Plasma
Quantum Logic for Trapped Atoms via Molecular Hyperfine Interactions
We study the deterministic entanglement of a pair of neutral atoms trapped in
an optical lattice by coupling to excited-state molecular hyperfine potentials.
Information can be encoded in the ground-state hyperfine levels and processed
by bringing atoms together pair-wise to perform quantum logical operations
through induced electric dipole-dipole interactions. The possibility of
executing both diagonal and exchange type entangling gates is demonstrated for
two three-level atoms and a figure of merit is derived for the fidelity of
entanglement. The fidelity for executing a CPHASE gate is calculated for two
87Rb atoms, including hyperfine structure and finite atomic localization. The
main source of decoherence is spontaneous emission, which can be minimized for
interaction times fast compared to the scattering rate and for sufficiently
separated atomic wavepackets. Additionally, coherent couplings to states
outside the logical basis can be constrained by the state dependent trapping
potential.Comment: Submitted to Physical Review
Multiparticle Entanglement in the Lipkin-Meshkov-Glick Model
The multiparticle entanglement in the Lipkin-Meshkov-Glick model has been
discussed extensively in this paper. Measured by the global entanglement and
its generalization, our calculation shows that the multiparticle entanglement
can faithfully detect quantum phase transitions. For an antiferromagnetic case
the multiparticle entanglement reaches the maximum at the transition point,
whereas for ferromagnetic coupling, two different behaviors of multiparticle
entanglement can be identified, dependent on the anisotropic parameter in the
coupling.Comment: 7 pages and 5 figure
Lower bounds on entanglement measures from incomplete information
How can we quantify the entanglement in a quantum state, if only the
expectation value of a single observable is given? This question is of great
interest for the analysis of entanglement in experiments, since in many
multiparticle experiments the state is not completely known. We present several
results concerning this problem by considering the estimation of entanglement
measures via Legendre transforms. First, we present a simple algorithm for the
estimation of the concurrence and extensions thereof. Second, we derive an
analytical approach to estimate the geometric measure of entanglement, if the
diagonal elements of the quantum state in a certain basis are known. Finally,
we compare our bounds with exact values and other estimation methods for
entanglement measures.Comment: 9 pages, 4 figures, v2: final versio
Genuine Multipartite Entanglement in Quantum Phase Transitions
We demonstrate that the Global Entanglement (GE) measure defined by Meyer and
Wallach, J. Math. Phys. 43, 4273 (2002), is maximal at the critical point for
the Ising chain in a transverse magnetic field. Our analysis is based on the
equivalence of GE to the averaged linear entropy, allowing the understanding of
multipartite entanglement (ME) features through a generalization of GE for
bipartite blocks of qubits. Moreover, in contrast to GE, the proposed ME
measure can distinguish three paradigmatic entangled states: ,
, and . As such the generalized measure can detect
genuine ME and is maximal at the critical point.Comment: 4 pages, 3 figures. Replaced with final published versio
Optical supercavitation in soft-matter
We investigate theoretically, numerically and experimentally nonlinear
optical waves in an absorbing out-of-equilibrium colloidal material at the
gelification transition. At sufficiently high optical intensity, absorption is
frustrated and light propagates into the medium. The process is mediated by the
formation of a matter-shock wave due to optically induced thermodiffusion, and
largely resembles the mechanism of hydrodynamical supercavitation, as it is
accompanied by a dynamic phase-transition region between the beam and the
absorbing material.Comment: 4 pages, 5 figures, revised version: corrected typos and reference
Efficient generation of random multipartite entangled states using time optimal unitary operations
We review the generation of random pure states using a protocol of repeated
two qubit gates. We study the dependence of the convergence to states with Haar
multipartite entanglement distribution. We investigate the optimal generation
of such states in terms of the physical (real) time needed to apply the
protocol, instead of the gate complexity point of view used in other works.
This physical time can be obtained, for a given Hamiltonian, within the
theoretical framework offered by the quantum brachistochrone formalism. Using
an anisotropic Heisenberg Hamiltonian as an example, we find that different
optimal quantum gates arise according to the optimality point of view used in
each case. We also study how the convergence to random entangled states depends
on different entanglement measures.Comment: 5 pages, 2 figures. New title, improved explanation of the algorithm.
To appear in Phys. Rev.
- …