The separability problem and normal completions. (Q1415288)

The author deals with the separability problem via a new normal completion problem. He shows that generically the \(N \times M\) separability problem may be reduced to a \((N-1) \times M\) separability problem via a multi-matrix normal completion problem. In particular he proves that the \(2 \times M\) separability is equivalent to a normal completion problem that is a variation of the one introduced by P. Halmos. In addition, the author obtains upper bounds on the number of states in a separable representation in terms of the normal completions.