We study quantum protocols among two distrustful parties. Under the
sole assumption of correctness - guaranteeing that honest players
obtain their correct outcomes - we show that every protocol
implementing a non-trivial primitive necessarily leaks information to
a dishonest player. This extends known impossibility results to all
non-trivial primitives. We provide a framework for quantifying this
leakage and argue that leakage is a good measure for the privacy
provided to the players by a given protocol. Our framework also covers
the case where the two players are helped by a trusted third party. We
show that despite the help of a trusted third party, the players
cannot amplify the cryptographic power of any primitive. All our
results hold even against quantum honest-but-curious adversaries who
honestly follow the protocol but purify their actions and apply a
different measurement at the end of the protocol. As concrete
examples, we establish lower bounds on the leakage of standard
universal two-party primitives such as oblivious transfer
