  In the present paper I formulate a framework that accommodates many
unambiguous discrimination problems. I show that the prior information about
any type of constituent (state, channel, or observable) allows us to
reformulate the discrimination among finite number of alternatives as the
discrimination among finite number of average constituents. Using this
framework I solve several unambiguous tasks. I present a solution to optimal
unambiguous comparison of two ensembles of unknown quantum states. I consider
two cases: 1) The two unknown states are arbitrary pure states of qudits. 2)
Alternatively, they are coherent states of single-mode optical fields. For this
case I propose simple and optimal experimental setup composed of beam-splitters
and a photodetector. As a second tasks I consider an unambiguous identification
(UI) of coherent states. In this task identical quantum systems are prepared in
coherent states and labeled as unknown and reference states, respectively. The
promise is that one reference state is the same as the unknown state and the
task is to find out unambiguously which one it is. The particular choice of the
reference states is unknown to us, and only the probability distribution
describing this choice is known. In a general case when multiple copies of
unknown and reference states are available I propose a scheme consisting of
beamsplitters and photodetectors that is optimal within linear optics. UI can
be considered as a search in a quantum database, whose elements are the
reference states and the query is represented by the unknown state. This
perspective motivated me to show that reference states can be recovered after
the measurement and might be used (with reduced success rate) in subsequent UI.
Moreover, I analyze the influence of noise in preparation of coherent states on
the performance of the proposed setup. Another problem I address is the
unambiguous comparison of a pair of unknown qudit unitary channels. I
characterize all solutions and identify the optimal ones. I prove that in
optimal experiments for comparison of unitary channels the entanglement is
necessary. The last task I studied is the unambiguous comparison of unknown
non-degenerate projective measurements. I distinguish between measurement
devices with apriori labeled and unlabeled outcomes. In both cases only the
difference of the measurements can be concluded unambiguously. For the labeled
case I derive the optimal strategy if each unknown measurement is used only
once. However, if the apparatuses are not labeled, then each measurement device
must be used (at least) twice. In particular, for qubit measurement apparatuses
with unlabeled outcomes I derive the optimal test state in the two-shots
scenario.
