  By establishing CHSH operators and CHSH-type inequalities, we show that any
entangled pure state in infinite-dimensional systems is entangled in a
$2\otimes2$ subspace. We find that, for infinite-dimensional systems, the
corresponding properties are similar to that of the two-qubit case: (i) The
CHSH-type inequalities provide a sufficient and necessary condition for
separability of pure states; (ii) The CHSH operators satisfy the Cirel'son
inequalities; (iii) Any state which violates one of these Bell inequalities is
distillable.
