36,411 research outputs found
Tensorial characterization and quantum estimation of weakly entangled qubits
In the case of two qubits, standard entanglement monotones like the linear
entropy fail to provide an efficient quantum estimation in the regime of weak
entanglement. In this paper, a more efficient entanglement estimation, by means
of a novel class of entanglement monotones, is proposed. Following an approach
based on the geometric formulation of quantum mechanics, these entanglement
monotones are defined by inner products on invariant tensor fields on bipartite
qubit orbits of the group SU(2)xSU(2).Comment: 23 pages, 3 figure
Efficient simulation of quantum evolution using dynamical coarse-graining
A novel scheme to simulate the evolution of a restricted set of observables
of a quantum system is proposed. The set comprises the spectrum-generating
algebra of the Hamiltonian. The idea is to consider a certain open-system
evolution, which can be interpreted as a process of weak measurement of the
distinguished observables performed on the evolving system of interest. Given
that the observables are "classical" and the Hamiltonian is moderately
nonlinear, the open system dynamics displays a large time-scales separation
between the dephasing of the observables and the decoherence of the evolving
state in the basis of the generalized coherent states (GCS), associated with
the spectrum-generating algebra. The time scale separation allows the unitary
dynamics of the observables to be efficiently simulated by the open-system
dynamics on the intermediate time-scale.The simulation employs unraveling of
the corresponding master equations into pure state evolutions, governed by the
stochastic nonlinear Schroedinger equantion (sNLSE). It is proved that GCS are
globally stable solutions of the sNLSE, if the Hamilonian is linear in the
algebra elements.Comment: The version submitted to Phys. Rev. A, 28 pages, 3 figures, comments
are very welcom
Left-invariant evolutions of wavelet transforms on the Similitude Group
Enhancement of multiple-scale elongated structures in noisy image data is
relevant for many biomedical applications but commonly used PDE-based
enhancement techniques often fail at crossings in an image. To get an overview
of how an image is composed of local multiple-scale elongated structures we
construct a multiple scale orientation score, which is a continuous wavelet
transform on the similitude group, SIM(2). Our unitary transform maps the space
of images onto a reproducing kernel space defined on SIM(2), allowing us to
robustly relate Euclidean (and scaling) invariant operators on images to
left-invariant operators on the corresponding continuous wavelet transform.
Rather than often used wavelet (soft-)thresholding techniques, we employ the
group structure in the wavelet domain to arrive at left-invariant evolutions
and flows (diffusion), for contextual crossing preserving enhancement of
multiple scale elongated structures in noisy images. We present experiments
that display benefits of our work compared to recent PDE techniques acting
directly on the images and to our previous work on left-invariant diffusions on
orientation scores defined on Euclidean motion group.Comment: 40 page
Measuring non-linear functionals of quantum harmonic oscillator states
Using only linear interactions and a local parity measurement we show how
entanglement can be detected between two harmonic oscillators. The scheme
generalizes to measure both linear and non-linear functionals of an arbitrary
oscillator state. This leads to many applications including purity tests,
eigenvalue estimation, entropy and distance measures - all without the need for
non-linear interactions or complete state reconstruction. Remarkably,
experimental realization of the proposed scheme is already within the reach of
current technology with linear optics.Comment: 5 pages, 2 figures. Minor corrections and some new references adde
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