3,546 research outputs found
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
Quantum origin of quantum jumps: Breaking of unitary symmetry induced by information transfer and the transition from quantum to classical
Measurements transfer information about a system to the apparatus, and then
further on -- to observers and (often inadvertently) to the environment. I show
that even imperfect copying essential in such situations restricts possible
unperturbed outcomes to an orthogonal subset of all possible states of the
system, thus breaking the unitary symmetry of its Hilbert space implied by the
quantum superposition principle. Preferred outcome states emerge as a result.
They provide framework for the ``wavepacket collapse'', designating terminal
points of quantum jumps, and defining the measured observable by specifying its
eigenstates. In quantum Darwinism, they are the progenitors of multiple copies
spread throughout the environment -- the fittest quantum states that not only
survive decoherence, but subvert it into carrying information about them --
into becoming a witness.Comment: For comments see Seth Lloyd, NATURE 450, 1167 (2007
Incoherent control and entanglement for two-dimensional coupled systems
We investigate accessibility and controllability of a quantum system S
coupled to a quantum probe P, both described by two-dimensional Hilbert spaces,
under the hypothesis that the external control affects only P. In this context
accessibility and controllability properties describe to what extent it is
possible to drive the state of the system S by acting on P and using the
interaction between the two systems. We give necessary and sufficient
conditions for these properties and we discuss the relation with the entangling
capability of the interaction between S and P. In particular, we show that
controllability can be expressed in terms of the SWAP operator, acting on the
composite system, and its square root.Comment: Latex, 13 page
Quantum Time: experimental multi-time correlations
In this paper we provide an experimental illustration of Page and Wootters'
quantum time mechanism that is able to describe two-time quantum correlation
functions. This allows us to test a Leggett-Garg inequality, showing a
violation from the "internal" observer point of view. The "external" observer
sees a time-independent global state. Indeed, the scheme is implemented using a
narrow-band single photon where the clock degree of freedom is encoded in the
photon's position. Hence, the internal observer that measures the position can
track the flow of time, while the external observer sees a delocalized photon
that has no time evolution in the experiment time-scale.Comment: 5 pages, 4 figure
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