  We consider how the theory of optimal quantum measurements determines the
maximum information available to the receiving party of a quantum key
distribution (QKD) system employing linearly independent but non-orthogonal
quantum states. Such a setting is characteristic of several practical QKD
protocols. Due to non-orthogonality, the receiver is not able to discriminate
unambiguously between the signals. To understand the fundamental limits that
this imposes, the quantity of interest is the maximum mutual information
between the transmitter (Alice) and the receiver, whether legitimate (Bob) or
an eavesdropper (Eve). To find the optimal measurement we use a framework based
on operator algebra and general results derived from singular value
decomposition, achieving optimal solutions for von Neumann measurements and
positive operator-valued measures (POVMs). The formal proof and quantitative
analysis elaborated for two signals allow one to conclude that optimal von
Neumann measurements are uniquely defined and provide a higher information gain
compared to POVMs. Interestingly, collective measurements not only do not
provide additional information gain with respect to individual ones, but also
suffer from a gain reduction in the case of POVMs.
