Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fundamental limitations in the purifications of tensor networks   We show a fundamental limitation in the description of quantum many-body
mixed states with tensor networks in purification form. Namely, we show that
there exist mixed states which can be represented as a translationally
invariant (TI) matrix product density operator (MPDO) valid for all system
sizes, but for which there does not exist a TI purification valid for all
system sizes. The proof is based on an undecidable problem and on the
uniqueness of canonical forms of matrix product states. The result also holds
for classical states.

26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin