  We analyze the properties of the conditional amplitude operator, the quantum
analog of the conditional probability which has been introduced in
[quant-ph/9512022]. The spectrum of the conditional operator characterizing a
quantum bipartite system is invariant under local unitary transformations and
reflects its inseparability. More specifically, it is shown that the
conditional amplitude operator of a separable state cannot have an eigenvalue
exceeding 1, which results in a necessary condition for separability. This
leads us to consider a related separability criterion based on the positive map
$\Gamma:\rho \to (Tr \rho) - \rho$, where $\rho$ is an Hermitian operator. Any
separable state is mapped by the tensor product of this map and the identity
into a non-negative operator, which provides a simple necessary condition for
separability. In the special case where one subsystem is a quantum bit,
$\Gamma$ reduces to time-reversal, so that this separability condition is
equivalent to partial transposition. It is therefore also sufficient for
$2\times 2$ and $2\times 3$ systems. Finally, a simple connection between this
map and complex conjugation in the "magic" basis is displayed.
