On the Power of Two-Party Quantum Cryptography

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 nontrivial 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 of a given protocol. Our framework also covers the case where the two players are helped by a trusted third party. We show that, even with 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 primitive such as oblivious transfer.