Quantum randomized encoding, verification of quantum computing, no-cloning, and blind quantum computing

Randomized encoding is a powerful cryptographic primitive with various applications such as secure multiparty computation, verifiable parallel cryptography, and complexity lower-bounds. Intuitively, randomized $\hat{f}$ of function $f$ another that $f(x)$ can be recovered from $\hat{f}(x)$, nothing except for leaked $\hat{f}(x)$. Its quantum version, encoding, has been introduced recently [Brakerski Yuen, arXiv:2006.01085]. $\hat{F}$ operation $F$ that, any state $\rho$, $F(\rho)$ $\hat{F}(\rho)$, $\hat{F}(\rho)$. In this paper, we show if BB84 generations possible an $E$, then two-round verification computing classical verifier who additionally do the $E$. One most important goals in field to construct protocol possible. This result therefore demonstrates potential application computing: find good (in terms complexity), computing. We, however, also too impossible: possible, no-cloning violated. We finally consider natural modification blind protocols way server gets output like encoding. modified not secure.