4,248 research outputs found
Boolean functions: noise stability, non-interactive correlation distillation, and mutual information
Let be the noise operator acting on Boolean functions , where is the noise parameter. Given
and fixed mean , which Boolean function has the
largest -th moment ? This question has
close connections with noise stability of Boolean functions, the problem of
non-interactive correlation distillation, and Courtade-Kumar's conjecture on
the most informative Boolean function. In this paper, we characterize
maximizers in some extremal settings, such as low noise (
is close to 0), high noise ( is close to 1/2), as well as
when is large. Analogous results are also established in
more general contexts, such as Boolean functions defined on discrete torus
and the problem of noise stability in a tree
model.Comment: Corrections of some inaccuracie
Blind Reconciliation
Information reconciliation is a crucial procedure in the classical
post-processing of quantum key distribution (QKD). Poor reconciliation
efficiency, revealing more information than strictly needed, may compromise the
maximum attainable distance, while poor performance of the algorithm limits the
practical throughput in a QKD device. Historically, reconciliation has been
mainly done using close to minimal information disclosure but heavily
interactive procedures, like Cascade, or using less efficient but also less
interactive -just one message is exchanged- procedures, like the ones based in
low-density parity-check (LDPC) codes. The price to pay in the LDPC case is
that good efficiency is only attained for very long codes and in a very narrow
range centered around the quantum bit error rate (QBER) that the code was
designed to reconcile, thus forcing to have several codes if a broad range of
QBER needs to be catered for. Real world implementations of these methods are
thus very demanding, either on computational or communication resources or
both, to the extent that the last generation of GHz clocked QKD systems are
finding a bottleneck in the classical part. In order to produce compact, high
performance and reliable QKD systems it would be highly desirable to remove
these problems. Here we analyse the use of short-length LDPC codes in the
information reconciliation context using a low interactivity, blind, protocol
that avoids an a priori error rate estimation. We demonstrate that 2x10^3 bits
length LDPC codes are suitable for blind reconciliation. Such codes are of high
interest in practice, since they can be used for hardware implementations with
very high throughput.Comment: 22 pages, 8 figure
Reaction Dynamics with Exotic Beams
We review the new possibilities offered by the reaction dynamics of
asymmetric heavy ion collisions, using stable and unstable beams. We show that
it represents a rather unique tool to probe regions of highly Asymmetric
Nuclear Matter () in compressed as well as dilute phases, and to test the
in-medium isovector interaction for high momentum nucleons. The focus is on a
detailed study of the symmetry term of the nuclear Equation of State () in
regions far away from saturation conditions but always under laboratory
controlled conditions.
Thermodynamic properties of are surveyed starting from nonrelativistic
and relativistic effective interactions. In the relativistic case the role of
the isovector scalar -meson is stressed. The qualitative new features
of the liquid-gas phase transition, "diffusive" instability and isospin
distillation, are discussed. The results of ab-initio simulations of n-rich,
n-poor, heavy ion collisions, using stochastic isospin dependent transport
equations, are analysed as a function of beam energy and centrality. The
isospin dynamics plays an important role in all steps of the reaction, from
prompt nucleon emissions to the final fragments. The isospin diffusion is also
of large interest, due to the interplay of asymmetry and density gradients. In
relativistic collisions, the possibility of a direct study of the covariant
structure of the effective nucleon interaction is shown. Results are discussed
for particle production, collective flows and iso-transparency.
Perspectives of further developments of the field, in theory as well as in
experiment, are presented.Comment: 167+5 pages, 77 figures, general revie
On reverse hypercontractivity
We study the notion of reverse hypercontractivity. We show that reverse
hypercontractive inequalities are implied by standard hypercontractive
inequalities as well as by the modified log-Sobolev inequality. Our proof is
based on a new comparison lemma for Dirichlet forms and an extension of the
Strook-Varapolos inequality.
A consequence of our analysis is that {\em all} simple operators L=Id-\E as
well as their tensors satisfy uniform reverse hypercontractive inequalities.
That is, for all and every positive valued function for we have . This should
be contrasted with the case of hypercontractive inequalities for simple
operators where is known to depend not only on and but also on the
underlying space.
The new reverse hypercontractive inequalities established here imply new
mixing and isoperimetric results for short random walks in product spaces, for
certain card-shufflings, for Glauber dynamics in high-temperatures spin systems
as well as for queueing processes. The inequalities further imply a
quantitative Arrow impossibility theorem for general product distributions and
inverse polynomial bounds in the number of players for the non-interactive
correlation distillation problem with -sided dice.Comment: Final revision. Incorporates referee's comments. The proof of
appendix B has been corrected. A shorter version of this article will appear
in GAF
Fundamental limits on concentrating and preserving tensorized quantum resources
Quantum technology offers great advantages in many applications by exploiting
quantum resources like nonclassicality, coherence, and entanglement. In
practice, an environmental noise unavoidably affects a quantum system and it is
thus an important issue to protect quantum resources from noise. In this work,
we investigate the manipulation of quantum resources possessing the so-called
tensorization property and identify the fundamental limitations on
concentrating and preserving those quantum resources. We show that if a
resource measure satisfies the tensorization property as well as the
monotonicity, it is impossible to concentrate multiple noisy copies into a
single better resource by free operations. Furthermore, we show that quantum
resources cannot be better protected from channel noises by employing
correlated input states on joint channels if the channel output resource
exhibits the tensorization property. We address several practical resource
measures where our theorems apply and manifest their physical meanings in
quantum resource manipulation.Comment: 12 pages, 3 figure
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