  Unambiguous (non-orthogonal) state discrimination (USD) has a fundamental
importance in quantum information and quantum cryptography. Various aspects of
two-state and multiple-state USD are studied here using singular value
decomposition (SVD) of the evolution operator that describes a given state
discriminating system. In particular, we relate the minimal angle between
states to the ratio of the minimal and maximal singular values. This is
supported by a simple geometrical picture in two-state USD. We apply our result
to study what states can undergo entanglement distillation in a given system.
