Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entanglement convertibility for infinite dimensional pure bipartite
  states   It is shown that the order property of pure bipartite states under SLOCC
(stochastic local operations and classical communications) changes radically
when dimensionality shifts from finite to infinite. In contrast to finite
dimensional systems where there is no pure incomparable state, the existence of
infinitely many mutually SLOCC incomparable states is shown for infinite
dimensional systems even under the bounded energy and finite information
exchange condition. These results show that the effect of the infinite
dimensionality of Hilbert space, the ``infinite workspace'' property, remains
even in physically relevant infinite dimensional systems.

2
The categories of this paper are: math
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas