Actively Secure Two-Party Evaluation of Any Quantum Operation

We provide the first two-party protocol allowing Alice and Bob to evaluate privately even against active adversaries any completely positive, tracepreserving map F ∈ L(Ain ⊗ Bin) → L(Aout ⊗ Bout), given as a quantum circuit, upon their joint quantum input state ρin ∈ D(Ain ⊗ Bin). Our protocol leaks no more to any active adversary than an ideal functionality for F provided Alice and Bob have the cryptographic resources for active secure two-party classical computation. Our protocol is constructed from the protocol for the same task secure against specious adversaries presented in [4].