  We report progress on the LU-LC conjecture - an open problem in the context
of entanglement in stabilizer states (or graph states). This conjecture states
that every two stabilizer states which are related by a local unitary
operation, must also be related by a local operation within the Clifford group.
The contribution of this paper is a reduction of the LU-LC conjecture to a
simpler problem - which, however, remains to date unsolved. As our main result,
we show that, if the LU-LC conjecture could be proved for the restricted case
of diagonal local unitary operations, then the conjecture is correct in its
totality. Furthermore, the reduced version of the problem, involving such
diagonal local operations, is mapped to questions regarding quadratic forms
over the finite field GF(2). Finally, we prove that correctness of the LU-LC
conjecture for stabilizer states implies a similar result for the more general
case of stabilizer codes.
