2,182 research outputs found
All Maximally Entangled Four Qubits States
We find an operational interpretation for the 4-tangle as a type of residual
entanglement, somewhat similar to the interpretation of the 3-tangle. Using
this remarkable interpretation, we are able to find the class of maximally
entangled four-qubits states which is characterized by four real parameters.
The states in the class are maximally entangled in the sense that their average
bipartite entanglement with respect to all possible bi-partite cuts is maximal.
We show that while all the states in the class maximize the average tangle,
there are only few states in the class that maximize the average Tsillas or
Renyi -entropy of entanglement. Quite remarkably, we find that up to
local unitaries, there exists two unique states, one maximizing the average
-Tsallis entropy of entanglement for all , while the
other maximizing it for all (including the von-Neumann case of
). Furthermore, among the maximally entangled four qubits states,
there are only 3 maximally entangled states that have the property that for 2,
out of the 3 bipartite cuts consisting of 2-qubits verses 2-qubits, the
entanglement is 2 ebits and for the remaining bipartite cut the entanglement
between the two groups of two qubits is 1ebit. The unique 3 maximally entangled
states are the 3 cluster states that are related by a swap operator. We also
show that the cluster states are the only states (up to local unitaries) that
maximize the average -Renyi entropy of entanglement for all .Comment: 15 pages, 2 figures, Revised Version: many references added, an
appendix added with a statement of the Kempf-Ness theore
Entanglement of subspaces in terms of entanglement of superpositions
We investigate upper and lower bounds on the entropy of entanglement of a
superposition of bipartite states as a function of the individual states in the
superposition. In particular, we extend the results in [G. Gour,
arxiv.org:0704.1521 (2007)] to superpositions of several states rather than
just two. We then investigate the entanglement in a subspace as a function of
its basis states: we find upper bounds for the largest entanglement in a
subspace and demonstrate that no such lower bound for the smallest entanglement
exists. Finally, we consider entanglement of superpositions using measures of
entanglement other than the entropy of entanglement.Comment: 7 pages, no figure
The sectional curvature remains positive when taking quotients by certain nonfree actions
We study some cases when the sectional curvature remains positive under the
taking of quotients by certain nonfree isometric actions of Lie groups. We
consider the actions of the groups and such that the quotient space
can be endowed with a smooth structure using the fibrations
and . We prove that the quotient space
carries a metric of positive sectional curvature, provided that the original
metric has positive sectional curvature on all 2-planes orthogonal to the
orbits of the action.Comment: 26 pages, 1 figure. Changed the spelling of the author's nam
Transfer of K-types on local theta lifts of characters and unitary lowest weight modules
In this paper we study representations of the indefinite orthogonal group
O(n,m) which are local theta lifts of one dimensional characters or unitary
lowest weight modules of the double covers of the symplectic groups. We apply
the transfer of K-types on these representations of O(n,m), and we study their
effects on the dual pair correspondences. These results provide examples that
the theta lifting is compatible with the transfer of K-types. Finally we will
use these results to study subquotients of some cohomologically induced
modules
- …