Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Necessary and sufficient condition for the existence of Schmidt
  decomposition in multipartite Hilbert spaces   Pati (Physics Letters A, 2000) derived a sufficient condition for the
existence of Schmidt decomposition in tripartite Hilbert spaces. In this paper,
we show that the condition is erroneous by demonstrating some counter-examples.
Moreover, we suitably modify the condition and provide a correctness proof. We
also show for the first time how this can be generalized to $n$-partite Hilbert
spaces for any $n\geq 2$. Finally, we prove that this condition is also a
necessary condition.

35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
1
The categories of this paper are: cs
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
2
The categories of this paper are: math
37
The categories of this paper are: supr-con