Privacy and correctness trade-offs for information-theoretically secure quantum homomorphic encryption

Quantum homomorphic encryption, which allows computation by a server directly on encrypted data, is fundamental primitive out of more complex quantum cryptography protocols can be built. For such constructions to possible, encryption must satisfy two privacy properties: data ensures that the input private from server, and circuit ciphertext after does not reveal any additional information about used perform it, beyond output itself. While well-studied in classical many schemes equipped with its analogue has received little attention. Here we establish definition for information-theoretic security. Furthermore, reduce oblivious transfer encryption. By using this reduction, our work unravels trade-offs between privacy, correctness broad family protocols, including allow only Clifford circuits.