Abstract
We address a general question whether geometry of submanifolds of an integral compact Kähler manifold is characterized by invariants that come from analysis. In geometric quantization, we have an integral compact Kähler manifold M and a holomorphic line bundle L on this manifold. There is a known procedure how to associate a sequence of mixed states ,
, to a submanifold Λ of M. Do analytic properties of this sequence reflect the geometry of Λ ? In this paper, we consider the case when M is a product of two integral compact Kähler manifolds. We show that, when Λ is a product submanifold of M, then the entanglement of formation of
is zero for all sufficiently large N.
Acknowledgments
N.W. was a research student of T.B. Research is supported in part by the Natural Sciences and Engineering Research Council of Canada
Disclosure statement
No potential conflict of interest was reported by the author(s).