25,472 research outputs found
Perfect single error-correcting codes in the Johnson Scheme
Delsarte conjectured in 1973 that there are no nontrivial pefect codes in the
Johnson scheme. Etzion and Schwartz recently showed that perfect codes must be
k-regular for large k, and used this to show that there are no perfect codes
correcting single errors in J(n,w) for n <= 50000. In this paper we show that
there are no perfect single error-correcting codes for n <= 2^250.Comment: 4 pages, revised, accepted for publication in IEEE Transactions on
Information Theor
Proposed observations of gravity waves from the early Universe via "Millikan oil drops"
Pairs of Planck-mass drops of superfluid helium coated by electrons (i.e.,
``Millikan oil drops''), when levitated in a superconducting magnetic trap, can
be efficient quantum transducers between electromagnetic (EM) and gravitational
(GR) radiation. This leads to the possibility of a Hertz-like experiment, in
which EM waves are converted at the source into GR waves, and then
back-converted at the receiver from GR waves back into EM waves. Detection of
the gravity-wave analog of the cosmic microwave background using these drops
can discriminate between various theories of the early Universe.Comment: 10 pages, 2 figures, NASA "Quantum-to-Cosmos" conference proceedings
to be published in IJMP
Algebraic Methods in the Congested Clique
In this work, we use algebraic methods for studying distance computation and
subgraph detection tasks in the congested clique model. Specifically, we adapt
parallel matrix multiplication implementations to the congested clique,
obtaining an round matrix multiplication algorithm, where
is the exponent of matrix multiplication. In conjunction
with known techniques from centralised algorithmics, this gives significant
improvements over previous best upper bounds in the congested clique model. The
highlight results include:
-- triangle and 4-cycle counting in rounds, improving upon the
triangle detection algorithm of Dolev et al. [DISC 2012],
-- a -approximation of all-pairs shortest paths in
rounds, improving upon the -round -approximation algorithm of Nanongkai [STOC 2014], and
-- computing the girth in rounds, which is the first
non-trivial solution in this model.
In addition, we present a novel constant-round combinatorial algorithm for
detecting 4-cycles.Comment: This is work is a merger of arxiv:1412.2109 and arxiv:1412.266
A one line factoring algorithm
We describe a variant of Fermat’s factoring algorithm which is competitive with SQUFOF in practice but has heuristic run time complexity O(n1/3) as a general factoring algorithm. We also describe a sparse class of integers for which the algorithm is particularly effective. We provide speed comparisons between an optimised implementation of the algorithm described and the tuned assortment of factoring algorithms in the Pari/GP computer algebra package
Heralded quantum entanglement between two crystals
Quantum networks require the crucial ability to entangle quantum nodes. A
prominent example is the quantum repeater which allows overcoming the distance
barrier of direct transmission of single photons, provided remote quantum
memories can be entangled in a heralded fashion. Here we report the observation
of heralded entanglement between two ensembles of rare-earth-ions doped into
separate crystals. A heralded single photon is sent through a 50/50
beamsplitter, creating a single-photon entangled state delocalized between two
spatial modes. The quantum state of each mode is subsequently mapped onto a
crystal, leading to an entangled state consisting of a single collective
excitation delocalized between two crystals. This entanglement is revealed by
mapping it back to optical modes and by estimating the concurrence of the
retrieved light state. Our results highlight the potential of rare-earth-ions
doped crystals for entangled quantum nodes and bring quantum networks based on
solid-state resources one step closer.Comment: 10 pages, 5 figure
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