5,566 research outputs found
Bell Violations through Independent Bases Games
In a recent paper, Junge and Palazuelos presented two two-player games
exhibiting interesting properties. In their first game, entangled players can
perform notably better than classical players. The quantitative gap between the
two cases is remarkably large, especially as a function of the number of inputs
to the players. In their second game, entangled players can perform notably
better than players that are restricted to using a maximally entangled state
(of arbitrary dimension). This was the first game exhibiting such a behavior.
The analysis of both games is heavily based on non-trivial results from Banach
space theory and operator space theory. Here we present two games exhibiting a
similar behavior, but with proofs that are arguably simpler, using elementary
probabilistic techniques and standard quantum information arguments. Our games
also give better quantitative bounds.Comment: Minor update
Double Centralizing Theorems for the Alternating Groups
Let be the -fold tensor product of a vector space
Following I. Schur we consider the action of the symmetric group on
by permuting coordinates. In the `super' ( graded)
case a sign is added [BR]. These actions give rise to
the corresponding Schur algebras S Here S is compared with
S the Schur algebra corresponding to the alternating subgroup
While in the `classical' (signless) case these two Schur
algebras are the same for large enough, it is proved that in the `super'
case where S is isomorphic to the
crossed-product algebra S SComment: 17 page
- β¦