  We present a quantum auction protocol using superpositions to represent bids
and distributed search to identify the winner(s). Measuring the final quantum
state gives the auction outcome while simultaneously destroying the
superposition. Thus non-winning bids are never revealed. Participants can use
entanglement to arrange for correlations among their bids, with the assurance
that this entanglement is not observable by others. The protocol is useful for
information hiding applications, such as partnership bidding with allocative
externality or concerns about revealing bidding preferences. The protocol
applies to a variety of auction types, e.g., first or second price, and to
auctions involving either a single item or arbitrary bundles of items (i.e.,
combinatorial auctions). We analyze the game-theoretical behavior of the
quantum protocol for the simple case of a sealed-bid quantum, and show how a
suitably designed adiabatic search reduces the possibilities for bidders to
game the auction. This design illustrates how incentive rather that
computational constraints affect quantum algorithm choices.
