Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterization of quantum entanglement via a hypercube of Segre
  embeddings   A particularly simple description of separability of quantum states arises
naturally in the setting of complex algebraic geometry, via the Segre
embedding. This is a map describing how to take products of projective Hilbert
spaces. In this paper, we show that for pure states of n particles, the
corresponding Segre embedding may be described by means of a directed hypercube
of dimension n-1, where all edges are bipartite-type Segre maps. Moreover, we
describe the image of the original Segre map via the intersections of images of
the n-1 edges whose target is the last vertex of the hypercube. This purely
algebraic result is then transferred to physics. For each of the last edges of
the Segre hypercube, we introduce an observable which measures geometric
separability and is related to the trace of the squared reduced density matrix.
As a consequence, the hypercube approach gives a novel viewpoint on measuring
entanglement, naturally relating bipartitions with $q$-partitions for q>1. We
test our observables against well-known states, showing that these provide
well-behaved and fine measures of entanglement.

28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin