  The Schr{\"o}dinger-Robertson inequality generally provides a stronger bound
on the product of uncertainties for two noncommuting observables than the
Heisenberg uncertainty relation, and as such, it can yield a stricter
separability condition in conjunction with partial transposition. In this
paper, using the Schr{\"o}dinger-Robertson uncertainty relation, the
separability condition previously derived from the su(2) and the su(1,1)
algebra is made stricter and refined to a form invariant with respect to local
phase shifts. Furthermore, a linear optical scheme is proposed to test this
invariant separability condition.
