12,518 research outputs found
Towards efficient decoding of classical-quantum polar codes
Known strategies for sending bits at the capacity rate over a general channel
with classical input and quantum output (a cq channel) require the decoder to
implement impractically complicated collective measurements. Here, we show that
a fully collective strategy is not necessary in order to recover all of the
information bits. In fact, when coding for a large number N uses of a cq
channel W, N I(W_acc) of the bits can be recovered by a non-collective strategy
which amounts to coherent quantum processing of the results of product
measurements, where I(W_acc) is the accessible information of the channel W. In
order to decode the other N (I(W) - I(W_acc)) bits, where I(W) is the Holevo
rate, our conclusion is that the receiver should employ collective
measurements. We also present two other results: 1) collective Fuchs-Caves
measurements (quantum likelihood ratio measurements) can be used at the
receiver to achieve the Holevo rate and 2) we give an explicit form of the
Helstrom measurements used in small-size polar codes. The main approach used to
demonstrate these results is a quantum extension of Arikan's polar codes.Comment: 21 pages, 2 figures, submission to the 8th Conference on the Theory
of Quantum Computation, Communication, and Cryptograph
Critical phenomena in the general spherically symmetric Einstein-Yang-Mills system
We study critical behavior in gravitational collapse of a general spherically
symmetric Yang-Mills field coupled to the Einstein equations. Unlike the
magnetic ansatz used in previous numerical work, the general Yang-Mills
connection has two degrees of freedom in spherical symmetry. This fact changes
the phenomenology of critical collapse dramatically. The magnetic sector
features both type I and type II critical collapse, with universal critical
solutions. In contrast, in the general system type I disappears and the
critical behavior at the threshold between dispersal and black hole formation
is always type II. We obtain values of the mass scaling and echoing exponents
close to those observed in the magnetic sector, however we find some
indications that the critical solution differs from the purely magnetic
discretely self-similar attractor and exact self-similarity and universality
might be lost. The additional "type III" critical phenomenon in the magnetic
sector, where black holes form on both sides of the threshold but the
Yang-Mills potential is in different vacuum states and there is a mass gap,
also disappears in the general system. We support our dynamical numerical
simulations with calculations in linear perturbation theory; for instance, we
compute quasi-normal modes of the unstable attractor (the Bartnik-McKinnon
soliton) in type I collapse in the magnetic sector.Comment: 15 pages, 15 figures; v2: matches published versio
The Post-Quasistatic Approximation as a test bed for Numerical Relativity
It is shown that observers in the standard ADM 3+1 treatment of matter are
the same as the observers used in the matter treatment of Bondi: they are
comoving and local Minkowskian. Bondi's observers are the basis of the
post--quasitatic approximation (PQSA) to study a contracting distribution of
matter. This correspondence suggests the possibility of using the PQSA as a
test bed for Numerical Relativity. The treatment of matter by the PQSA and its
connection with the ADM 3+1 treatment are presented, for its practical use as a
calibration tool and as a test bed for numerical relativistic hydrodynamic
codes.Comment: 4 pages; to appear as a Brief Report in Physical Review
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