Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The prime factorization property of entangled quantum states   Completely entangled quantum states are shown to factorize into tensor
products of entangled states whose dimensions are powers of prime numbers. The
entangled states of each prime-power dimension transform among themselves under
a finite Heisenberg group. We are thus led to examine processes in which
factors are exchanged between entangled states and so consider canonical
ensembles in which these processes occur. It is shown that the Riemann zeta
function is the appropriate partition function and that the Riemann hypothesis
makes a prediction about the high temperature contribution of modes of large
dimension.

12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
2
The categories of this paper are: math
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas