3,490 research outputs found
Limits of elliptic hypergeometric integrals
In math.QA/0309252, the author proved a number of multivariate elliptic
hypergeometric integrals. The purpose of the present note is to explore more
carefully the various limiting cases (hyperbolic, trigonometric, rational, and
classical) that exist. In particular, we show (using some new estimates of
generalized gamma functions) that the hyperbolic integrals (previously treated
as purely formal limits) are indeed limiting cases. We also obtain a number of
new trigonometric (q-hypergeometric) integral identities as limits from the
elliptic level.Comment: 41 pages LaTeX. Minor stylistic changes, statement of Theorem 4.7
fixe
On bound entanglement assisted distillation
We investigate asymptotic distillation of entanglement in the presence of an
unlimited amount of bound entanglement for bi-partite systems. We show that the
distillability is still bounded by the relative entropy of entanglement. This
offers a strong support to the fact that bound entanglement does not improve
distillation of entanglement.Comment: 9 pages, no figures, minor typos correcte
A semidefinite program for distillable entanglement
We show that the maximum fidelity obtained by a p.p.t. distillation protocol
is given by the solution to a certain semidefinite program. This gives a number
of new lower and upper bounds on p.p.t. distillable entanglement (and thus new
upper bounds on 2-locally distillable entanglement). In the presence of
symmetry, the semidefinite program simplifies considerably, becoming a linear
program in the case of isotropic and Werner states. Using these techniques, we
determine the p.p.t. distillable entanglement of asymmetric Werner states and
``maximally correlated'' states. We conclude with a discussion of possible
applications of semidefinite programming to quantum codes and 1-local
distillation.Comment: 28 pages, LaTe
A difference-integral representation of Koornwinder polynomials
We construct new families of (q-) difference and (contour) integral operators
having nice actions on Koornwinder's multivariate orthogonal polynomials. We
further show that the Koornwinder polynomials can be constructed by suitable
sequences of these operators applied to the constant polynomial 1, giving the
difference-integral representation of the title. Macdonald's conjectures (as
proved by van Diejen and Sahi) for the principal specialization and norm follow
immediately, as does a Cauchy-type identity of Mimachi.Comment: 15 pages AMSLaTeX. To appear in proceedings of the Workshop on Jack,
Hall-Littlewood and Macdonald polynomials (September 2003, ICMS
Monotonicity of the quantum linear programming bound
The most powerful technique known at present for bounding the size of quantum
codes of prescribed minimum distance is the quantum linear programming bound.
Unlike the classical linear programming bound, it is not immediately obvious
that if the quantum linear programming constraints are satisfiable for
dimension K, that the constraints can be satisfied for all lower dimensions. We
show that the quantum linear programming bound is indeed monotonic in this
sense, and give an explicitly monotonic reformulation.Comment: 5 pages, AMSTe
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