125,333 research outputs found
Long Range Scattering and Modified Wave Operators for some Hartree Type Equations
We study the theory of scattering for a class of Hartree type equations with
long range interactions in space dimension n > 2, including Hartree equations
with potential V(x) = lambda |x|^{- gamma} with gamma < 1. For 1/2 < gamma < 1
we prove the existence of modified wave operators with no size restriction on
the data and we determine the asymptotic behaviour in time of solutions in the
range of the wave operators.Comment: TeX, 89 pages, available http://qcd.th.u-psud.f
Group theoretical study of LOCC-detection of maximally entangled state using hypothesis testing
In the asymptotic setting, the optimal test for hypotheses testing of the
maximally entangled state is derived under several locality conditions for
measurements. The optimal test is obtained in several cases with the asymptotic
framework as well as the finite-sample framework. In addition, the experimental
scheme for the optimal test is presented
Unitary-process discrimination with error margin
We investigate a discrimination scheme between unitary processes. By
introducing a margin for the probability of erroneous guess, this scheme
interpolates the two standard discrimination schemes: minimum-error and
unambiguous discrimination. We present solutions for two cases. One is the case
of two unitary processes with general prior probabilities. The other is the
case with a group symmetry: the processes comprise a projective representation
of a finite group. In the latter case, we found that unambiguous discrimination
is a kind of "all or nothing": the maximum success probability is either 0 or
1. We also closely analyze how entanglement with an auxiliary system improves
discrimination performance.Comment: 9 pages, 3 figures, presentation improved, typos corrected, final
versio
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