133 research outputs found
Successive vertex orderings of fully regular graphs
A graph G = (V,E) is called fully regular if for every independent set
, the number of vertices in I that are not connected
to any element of I depends only on the size of I. A linear ordering of the
vertices of G is called successive if for every i, the first i vertices induce
a connected subgraph of G. We give an explicit formula for the number of
successive vertex orderings of a fully regular graph.
As an application of our results, we give alternative proofs of two theorems
of Stanley and Gao + Peng, determining the number of linear edge orderings of
complete graphs and complete bipartite graphs, respectively, with the property
that the first i edges induce a connected subgraph. As another application, we
give a simple product formula for the number of linear orderings of the
hyperedges of a complete 3-partite 3-uniform hypergraph such that, for every i,
the first i hyperedges induce a connected subgraph. We found similar formulas
for complete (non-partite) 3-uniform hypergraphs and in another closely related
case, but we managed to verify them only when the number of vertices is small.Comment: 14 page
Experimental preparation and verification of quantum money
A quantum money scheme enables a trusted bank to provide untrusted users with
verifiable quantum banknotes that cannot be forged. In this work, we report an
experimental demonstration of the preparation and verification of unforgeable
quantum banknotes. We employ a security analysis that takes experimental
imperfections fully into account. We measure a total of states
in one verification round, limiting the forging probability to based
on the security analysis. Our results demonstrate the feasibility of preparing
and verifying quantum banknotes using currently available experimental
techniques.Comment: 12 pages, 4 figure
Energy-Time Entanglement-based Dispersive Optics Quantum Key Distribution over Optical Fibers of 20 km
An energy-time entanglement-based dispersive optics quantum key distribution
(DO-QKD) is demonstrated experimentally over optical fibers of 20 km. In the
experiment, the telecom band energy-time entangled photon pairs are generated
through spontaneous four wave mixing in a silicon waveguide. The arrival time
of photons are registered for key generating and security test. High
dimensional encoding in the arrival time of photons is used to increase the
information per coincidence of photon pairs. The bin sifting process is
optimized by a three level structure, which significantly reduces the raw
quantum bit error rate (QBER) due to timing jitters of detectors and
electronics. A raw key generation rate of 151kbps with QBER of 4.95% is
achieved, under a time-bin encoding format with 4 bits per coincidence. This
experiment shows that entanglement-based DO-QKD can be implemented in an
efficient and convenient way, which has great potential in quantum secure
communication networks in the future
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