Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum codes give counterexamples to the unique pre-image conjecture of
  the N-representability problem   It is well known that the ground state energy of many-particle Hamiltonians
involving only 2-body interactions can be obtained using constrained
optimizations over density matrices which arise from reducing an N-particle
state. While determining which 2-particle density matrices are "N-
representable" is a computationally hard problem, all known extreme
N-representable 2-particle reduced density matrices arise from a unique
N-particle pre-image, satisfying a conjecture established in 1972. We present
explicit counterexamples to this conjecture through giving Hamiltonians with
2-body interactions which have degenerate ground states that cannot be
distinguished by any 2-body operator. We relate the existence of such
counterexamples to quantum error correction codes and topologically ordered
spin systems.

10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
2
The categories of this paper are: math
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an