Factoring a quantum state

Question

I\'m looking for algorithms that take an arbitrary quantum state made up of a sum of weighted classical states made up of bits, like this:

|0000>/2 - |0011>         


        

Answer 1

It looks like an efficient algorithm is going to be hard:

From wikipedia:

The problem of deciding whether a state is separable in general is sometimes called the separability problem in quantum information theory. It is considered to be a difficult problem. It has been shown to be NP-hard.

Gurvits, L., Classical deterministic complexity of Edmonds’ problem and quantum entanglement, in Proceedings of the 35th ACM Symposium on Theory of Computing, ACM Press, New York, 2003.

Sevag Gharibian, Strong NP-Hardness of the Quantum Separability Problem, Quantum Information and Computation, Vol. 10, No. 3&4, pp. 343-360, 2010. arXiv:0810.4507