InSeparableBall

InSeparableBall is a function that determines whether or not a density matrix is contained within the ball of states that are separable centered at the maximally-mixed state (more generally, it determines whether or not a positive semidefinite operator is within the ball of separability centered at an appropriately-scaled identity matrix). The size of this ball of separability was computed in.

Syntax

 * ISB = InSeparableBall(X)

Argument descriptions

 * X: A bipartite density matrix (or any bipartite positive semidefinite operator).

Examples
The only states acting on $\mathbb{C}^m \otimes \mathbb{C}^n$ in the separable ball that do not have full rank are those with exactly 1 zero eigenvalue, and the $mn-1$ non-zero eigenvalues equal to each other. The following code highlights this fact when $m = n = 2$: