Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Criterion of Local Unitary Equivalence for Multipartite States   We study the local unitary equivalence of arbitrary dimensional multipartite
quantum mixed states. We present a necessary and sufficient criterion of the
local unitary equivalence for general multipartite states based on matrix
realignment. The criterion is shown to be operational even for particularly
degenerated states by detailed examples. Besides, explicit expressions of the
local unitary operators are constructed for locally equivalent states. In
complement to the criterion, an alternative approach based on partial
transposition of matrices is also given, which makes the criterion more
effective in dealing with generally degenerated mixed states.

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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
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The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
3
The categories of this paper are: physics