Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mutually Unbiased Product Bases for Multiple Qudits   We investigate the interplay between mutual unbiasedness and product bases
for multiple qudits of possibly different dimensions. A product state of such a
system is shown to be mutually unbiased to a product basis only if each of its
factors is mutually unbiased to all the states which occur in the corresponding
factors of the product basis. This result implies both a tight limit on the
number of mutually unbiased product bases which the system can support and a
complete classification of mutually unbiased product bases for multiple qubits
or qutrits. In addition, only maximally entangled states can be mutually
unbiased to a maximal set of mutually unbiased product bases.

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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org