  We present a set of inequalities for detecting quantum entanglement of
$2\otimes d$ quantum states. For $2\otimes 2$ and $2\otimes 3$ systems, the
inequalities give rise to sufficient and necessary separability conditions for
both pure and mixed states. For the case of $d>3$, these inequalities are
necessary conditions for separability, which detect all entangled states that
are not positive under partial transposition and even some entangled states
with positive partial transposition. These inequalities are given by mean
values of local observables and present an experimental way of detecting the
quantum entanglement of $2\otimes d$ quantum states and even multi-qubit pure
states.
