  Quantum retrodiction is a time-symmetric approach to quantum mechanics with
applications in a number of important problems. One of the major challenges to
its more widespread applicability is the restriction of its symmetric formalism
to unbiased sources. The main result of this paper is to develop a general
theory yielding a symmetric formalism for arbitrary sources. We then highlight
on a specific example, by presenting the optimal solution to the retrodiction
problem that is dual to unambiguous state discrimination, how the generalized
approach works. We also show how this formalism leads to a symmetric
formulation of the communication channel between Alice and Bob and point to the
intrinsic connection between retrodiction and the no-signaling principle.
