1,914 research outputs found
On cyclic branched coverings of prime knots
We prove that a prime knot K is not determined by its p-fold cyclic branched
cover for at most two odd primes p. Moreover, we show that for a given odd
prime p, the p-fold cyclic branched cover of a prime knot K is the p-fold
cyclic branched cover of at most one more knot K' non equivalent to K. To prove
the main theorem, a result concerning the symmetries of knots is also obtained.
This latter result can be interpreted as a characterisation of the trivial
knot.Comment: 28 pages, 2 figure
Optimal State Merging Without Decoupling
We construct an optimal state merging protocol by adapting a
recently-discovered optimal entanglement distillation protcol [Renes and
Boileau, Phys. Rev. A . 73, 032335 (2008)]. The proof of optimality relies only
on directly establishing sufficient "amplitude" and "phase" correlations
between Alice and Bob and not on usual techniques of decoupling Alice from the
environment. This strengthens the intuition from quantum error-correction that
these two correlations are all that really matter in two-party quantum
information processing.Comment: 10 pages, accepted contribution to TQC 200
Conjectured Strong Complementary Information Tradeoff
We conjecture a new entropic uncertainty principle governing the entropy of
complementary observations made on a system given side information in the form
of quantum states, generalizing the entropic uncertainty relation of Maassen
and Uffink [Phys. Rev. Lett. 60, 1103 (1988)]. We prove a special case for
certain conjugate observables by adapting a similar result found by Christandl
and Winter pertaining to quantum channels [IEEE Trans. Inf. Theory 51, 3159
(2005)], and discuss possible applications of this result to the decoupling of
quantum systems and for security analysis in quantum cryptography.Comment: 4 page
Scholarship Reconsidered: A Challenge to Use Teaching Portfolios to Document the Scholarship of Teaching
This article examines the use of teaching portfolios in documenting the scholarship of teaching in the U.S. Portfolios are generally three-ring binders that create teaching records including most often three types of materials: products of good teaching; material from oneself; materials from others. The major contribution most advocates of portfolios mention is the perceived improvement of teaching. Portfolios increase reflection and action about teaching by: giving focus on teaching as part of a professor\u27s expected activities; encouraging faculty to seek ways to improve their teaching by attending conference meetings on teaching, reading about teaching techniques, and creating discussions about teaching within the department and university; and stimulating formal and informal research on teaching
Robust Quantum Communication Using A Polarization-Entangled Photon Pair
Noise and imperfection of realistic devices are major obstacles for
implementing quantum cryptography. In particular birefringence in optical
fibers leads to decoherence of qubits encoded in polarization of photon. We
show how to overcome this problem by doing single qubit quantum communication
without a shared spatial reference frame and precise timing. Quantum
information will be encoded in pair of photons using ``tag'' operations which
corresponds to the time delay of one of the polarization modes. This method is
robust against the phase instability of the interferometers despite the use of
time-bins. Moreover synchronized clocks are not required in the ideal situation
no photon loss case as they are only necessary to label the different encoded
qubits.Comment: 4 pages, 2 figure
Unconditional Security of Three State Quantum Key Distribution Protocols
Quantum key distribution (QKD) protocols are cryptographic techniques with
security based only on the laws of quantum mechanics. Two prominent QKD schemes
are the BB84 and B92 protocols that use four and two quantum states,
respectively. In 2000, Phoenix et al. proposed a new family of three state
protocols that offers advantages over the previous schemes. Until now, an error
rate threshold for security of the symmetric trine spherical code QKD protocol
has only been shown for the trivial intercept/resend eavesdropping strategy. In
this paper, we prove the unconditional security of the trine spherical code QKD
protocol, demonstrating its security up to a bit error rate of 9.81%. We also
discuss on how this proof applies to a version of the trine spherical code QKD
protocol where the error rate is evaluated from the number of inconclusive
events.Comment: 4 pages, published versio
On abstract commensurators of groups
We prove that the abstract commensurator of a nonabelian free group, an
infinite surface group, or more generally of a group that splits appropriately
over a cyclic subgroup, is not finitely generated.
This applies in particular to all torsion-free word-hyperbolic groups with
infinite outer automorphism group and abelianization of rank at least 2.
We also construct a finitely generated, torsion-free group which can be
mapped onto Z and which has a finitely generated commensurator.Comment: 13 pages, no figur
Topological Symmetry Groups of K_{4r+3}
We present the concept of the topological symmetry group as a way to analyze
the symmetries of non-rigid molecules. Then we characterize all of the groups
which can occur as the topological symmetry group of an embedding of the
complete graph K_{4r+3} in S^3
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