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, trace-preserving map $$\mathscr {F} \in \mathrm {L}\mathcal {A}_{{{\mathrm{in}}}} \otimes \mathcal {B}_{{{\mathrm{in}}}} \rightarrow $$$$\mathrm {L}\mathcal {A}_{{{\mathrm{out}}}} \otimes \mathcal {B}_{{{\mathrm{out}}}}$$, given as a quantum circuit, upon their joint quantum input state $$\rho _{\mathrm {in}}\in \mathrm{D}{\mathcal {A}_{{{\mathrm{in}}}} \otimes \mathcal {B}_{{{\mathrm{in}}}}}$$. Our protocol leaks no more to any active adversary than an ideal functionality for $$\mathscr {F}$$ 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].

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