  Oblivious transfer (OT) is a fundamental primitive for secure two-party
computation. It is well known that OT cannot be implemented with
information-theoretic security if the two players only have access to noiseless
communication channels, even in the quantum case. As a result, weaker variants
of OT have been studied. In this work, we rigorously establish the
impossibility of cheat-sensitive OT, where a dishonest party can cheat, but
risks being detected. We construct a general attack on any quantum protocol
that allows the receiver to compute all inputs of the sender and provide an
explicit upper bound on the success probability of this attack. This implies
that cheat-sensitive quantum Symmetric Private Information Retrieval cannot be
implemented with statistical information-theoretic security. Leveraging the
techniques devised for our proofs, we provide entropic bounds on primitives
needed for secure function evaluation. They imply impossibility results for
protocols where the players have access to OT as a resource. This result
significantly improves upon existing bounds and yields tight bounds for
reductions of 1-out-of-n OT to a resource primitive. Our results hold in
particular for transformations between a finite number of primitives and for
any error.
