38,024 research outputs found
How often is a random quantum state k-entangled?
The set of trace preserving, positive maps acting on density matrices of size
d forms a convex body. We investigate its nested subsets consisting of
k-positive maps, where k=2,...,d. Working with the measure induced by the
Hilbert-Schmidt distance we derive asymptotically tight bounds for the volumes
of these sets. Our results strongly suggest that the inner set of
(k+1)-positive maps forms a small fraction of the outer set of k-positive maps.
These results are related to analogous bounds for the relative volume of the
sets of k-entangled states describing a bipartite d X d system.Comment: 19 pages in latex, 1 figure include
The D2-D6 System and a Fibered AdS Geometry
The system of D2 branes localized on or near D6 branes is considered. The
world-volume theory on the D2 branes is investigated, using its conjectured
relation to the near-horizon geometry. The results are in agreement with known
facts and expectations for the corresponding field theory and a rich phase
structure is obtained as a function of the energy scale and the number of
branes. In particular, for an intermediate range of the number of D6 branes,
the IR geometry is that of an AdS_4 space fibered over a compact space. This
D2-D6 system is compared to other systems, related to it by compactification
and duality and it is shown that the qualitative differences have compatible
explanations in the geometric and field-theoretic descriptions. Another system
-- that of NS5 branes located at D6 branes -- is also briefly studied, leading
to a similar phase structure.Comment: 35 pages (Latex) and 2 figures (encapsulated postscript). Ver2: added
discussion of the relation to the system without D6 branes (in the
introduction and in figure 1); added description of the geometrical
realization of the R symmetries (in section 3.1
A Note on c=1 Virasoro Boundary States and Asymmetric Shift Orbifolds
We comment on the conformal boundary states of the c=1 free boson theory on a
circle which do not preserve the U(1) symmetry. We construct these Virasoro
boundary states at a generic radius by a simple asymmetric shift orbifold
acting on the fundamental boundary states at the self-dual radius. We further
calculate the boundary entropy and find that the Virasoro boundary states at
irrational radius have infinite boundary entropy. The corresponding open string
description of the asymmetric orbifold is given using the quotient algebra
construction. Moreover, we find that the quotient algebra associated with a
non-fundamental boundary state contains the noncommutative Weyl algebra.Comment: 21 pages, harvmac; v2: minor clarification in section 3.4; v3: a
discussion on cocycles added in section 2, and low energy limit mistake
removed and clarifications added in section 4.
Exceptional hyperbolic 3-manifolds
We correct and complete a conjecture of D. Gabai, R. Meyerhoff and N.
Thurston on the classification and properties of thin tubed closed hyperbolic
3-manifolds. We additionally show that if N is a closed hyperbolic 3-manifold,
then either N=Vol3 or N contains a closed geodesic that is the core of an
embedded tube of radius log(3)/2.Comment: 22 pages, 2 figure
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