  The (negative-weighted) quantum adversary bound is a tight characterisation
of the quantum query complexity for any partial function. We analyse the extent
to which this bound can be generalised. Ambainis et al. [arXiv:1012.2112] and
Lee et al. [arXiv:1011.3020] generalised this bound to the state generation and
state conversion problems, respectively. Using the ideas by Lee et al., we get
even further generalisations of the bound.
  We obtain a version of the bound for general input oracles, which are just
arbitrary unitaries. We also generalise the bound to the problem of
implementing arbitrary unitary transformations. Similarly to the bound by Lee
et al., our bound is a lower bound for exact transformation and an upper bound
for approximate transformation. This version of the bound possesses the tight
composition property.
  Using this construction, we also obtain lower bounds on the quantum query
complexity of functions and relations with general input oracles.
