19,297 research outputs found
Physical properties of the Schur complement of local covariance matrices
General properties of global covariance matrices representing bipartite
Gaussian states can be decomposed into properties of local covariance matrices
and their Schur complements. We demonstrate that given a bipartite Gaussian
state described by a covariance matrix \textbf{V}, the
Schur complement of a local covariance submatrix of it can be
interpreted as a new covariance matrix representing a Gaussian operator of
party 1 conditioned to local parity measurements on party 2. The connection
with a partial parity measurement over a bipartite quantum state and the
determination of the reduced Wigner function is given and an operational
process of parity measurement is developed. Generalization of this procedure to
a -partite Gaussian state is given and it is demonstrated that the
system state conditioned to a partial parity projection is given by a
covariance matrix such as its block elements are Schur complements
of special local matrices.Comment: 10 pages. Replaced with final published versio
Evolution of Privacy Loss in Wikipedia
The cumulative effect of collective online participation has an important and
adverse impact on individual privacy. As an online system evolves over time,
new digital traces of individual behavior may uncover previously hidden
statistical links between an individual's past actions and her private traits.
To quantify this effect, we analyze the evolution of individual privacy loss by
studying the edit history of Wikipedia over 13 years, including more than
117,523 different users performing 188,805,088 edits. We trace each Wikipedia's
contributor using apparently harmless features, such as the number of edits
performed on predefined broad categories in a given time period (e.g.
Mathematics, Culture or Nature). We show that even at this unspecific level of
behavior description, it is possible to use off-the-shelf machine learning
algorithms to uncover usually undisclosed personal traits, such as gender,
religion or education. We provide empirical evidence that the prediction
accuracy for almost all private traits consistently improves over time.
Surprisingly, the prediction performance for users who stopped editing after a
given time still improves. The activities performed by new users seem to have
contributed more to this effect than additional activities from existing (but
still active) users. Insights from this work should help users, system
designers, and policy makers understand and make long-term design choices in
online content creation systems
Uniform approximation for the overlap caustic of a quantum state with its translations
The semiclassical Wigner function for a Bohr-quantized energy eigenstate is
known to have a caustic along the corresponding classical closed phase space
curve in the case of a single degree of freedom. Its Fourier transform, the
semiclassical chord function, also has a caustic along the conjugate curve
defined as the locus of diameters, i.e. the maximal chords of the original
curve. If the latter is convex, so is its conjugate, resulting in a simple fold
caustic. The uniform approximation through this caustic, that is here derived,
describes the transition undergone by the overlap of the state with its
translation, from an oscillatory regime for small chords, to evanescent
overlaps, rising to a maximum near the caustic. The diameter-caustic for the
Wigner function is also treated.Comment: 14 pages, 9 figure
Sherrington-Kirkpatrick model near : expanding around the Replica Symmetric Solution
An expansion for the free energy functional of the Sherrington-Kirkpatrick
(SK) model, around the Replica Symmetric SK solution is investigated. In particular, when the
expansion is truncated to fourth order in. . The
Full Replica Symmetry Broken (FRSB) solution is explicitly found but it turns
out to exist only in the range of temperature , not
including T=0. On the other hand an expansion around the paramagnetic solution
up to fourth order yields a FRSB solution
that exists in a limited temperature range .Comment: 18 pages, 3 figure
Semiclassical Evolution of Dissipative Markovian Systems
A semiclassical approximation for an evolving density operator, driven by a
"closed" hamiltonian operator and "open" markovian Lindblad operators, is
obtained. The theory is based on the chord function, i.e. the Fourier transform
of the Wigner function. It reduces to an exact solution of the Lindblad master
equation if the hamiltonian operator is a quadratic function and the Lindblad
operators are linear functions of positions and momenta.
Initially, the semiclassical formulae for the case of hermitian Lindblad
operators are reinterpreted in terms of a (real) double phase space, generated
by an appropriate classical double Hamiltonian. An extra "open" term is added
to the double Hamiltonian by the non-hermitian part of the Lindblad operators
in the general case of dissipative markovian evolution. The particular case of
generic hamiltonian operators, but linear dissipative Lindblad operators, is
studied in more detail. A Liouville-type equivariance still holds for the
corresponding classical evolution in double phase, but the centre subspace,
which supports the Wigner function, is compressed, along with expansion of its
conjugate subspace, which supports the chord function.
Decoherence narrows the relevant region of double phase space to the
neighborhood of a caustic for both the Wigner function and the chord function.
This difficulty is avoided by a propagator in a mixed representation, so that a
further "small-chord" approximation leads to a simple generalization of the
quadratic theory for evolving Wigner functions.Comment: 33 pages - accepted to J. Phys.
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