Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Structure of Qubit Unextendible Product Bases   Unextendible product bases have been shown to have many important uses in
quantum information theory, particularly in the qubit case. However, very
little is known about their mathematical structure beyond three qubits. We
present several new results about qubit unextendible product bases, including a
complete characterization of all four-qubit unextendible product bases, which
we show there are exactly 1446 of. We also show that there exist p-qubit UPBs
of almost all sizes less than $2^p$.

28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an