  We address the problem of unambiguous discrimination among oracle operators.
The general theory of unambiguous discrimination among unitary operators is
extended with this application in mind. We prove that entanglement with an
ancilla cannot assist any discrimination strategy for commuting unitary
operators. We also obtain a simple, practical test for the unambiguous
distinguishability of an arbitrary set of unitary operators on a given system.
Using this result, we prove that the unambiguous distinguishability criterion
is the same for both standard and minimal oracle operators. We then show that,
except in certain trivial cases, unambiguous discrimination among all standard
oracle operators corresponding to integer functions with fixed domain and range
is impossible. However, we find that it is possible to unambiguously
discriminate among the Grover oracle operators corresponding to an arbitrarily
large unsorted database. The unambiguous distinguishability of standard oracle
operators corresponding to totally indistinguishable functions, which possess a
strong form of classical indistinguishability, is analysed. We prove that these
operators are not unambiguously distinguishable for any finite set of totally
indistinguishable functions on a Boolean domain and with arbitrary fixed range.
Sets of such functions on a larger domain can have unambiguously
distinguishable standard oracle operators and we provide a complete analysis of
the simplest case, that of four functions. We also examine the possibility of
unambiguous oracle operator discrimination with multiple parallel calls and
investigate an intriguing unitary superoperator transformation between standard
and entanglement-assisted minimal oracle operators.
