Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum States and Hardy's Formulation of the Uncertainty Principle : a
  Symplectic Approach   We express the condition for a phase space Gaussian to be the Wigner
distribution of a mixed quantum state in terms of the symplectic capacity of
the associated Wigner ellipsoid. Our results are motivated by Hardy's
formulation of the uncertainty principle for a function and its Fourier
transform. As a consequence we are able to state a more general form of Hardy's
theorem.

14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs