论文标题
量子随机编码，量子计算的验证，无键和盲量计算
Quantum randomized encoding, verification of quantum computing, no-cloning, and blind quantum computing
论文作者
论文摘要
随机编码是一种功能强大的加密原始性，具有各种应用，例如安全的多方计算，可验证的计算，并行密码学和复杂性下限。直观地，函数$ f $的随机编码$ \ hat {f} $是另一个函数，因此可以从$ \ hat {f}（x）$中恢复$ f（x）$，除了$ f（x）$以外，从$ \ hat Hat {f}（f}（x）$中泄漏了$ f（x）$。最近引入了它的量子版本，即量子随机编码[Brakerski and Yuen，arxiv：2006.01085]。量子操作$ f $的量子随机编码$ \ hat {f} $是另一个量子操作，因此，对于任何量子状态$ρ$，$ f（ρ）$可以从$ \ hat {f}（ρ）$中恢复，除了$ f（ρ）$以外，没有什么都没有泄漏从$ f（ρ）$泄漏从$ \ hat f hat {f} $。在本文中，我们表明，如果使用编码操作$ e $对BB84状态的量子随机编码是可能的，那么可以使用经典验证器进行两轮量子计算的验证，而经典验证者可以另外进行操作$ e $。量子计算验证领域中最重要的目标之一是用验证者尽可能经典地构建验证协议。因此，该结果证明了量子随机编码的潜在应用到量子计算的验证：如果我们可以找到良好的量子随机编码（就编码复杂性而言），那么我们可以构建量子计算的良好验证协议。但是，我们还表明，太量子随机编码是不可能的：如果可以使用经典编码操作进行量子随机编码，则违反了无粘结。我们最终以一种自然的修改对盲量计算协议进行了自然修改，以使服务器像量子随机编码一样输出。我们表明修改后的协议不安全。
Randomized encoding is a powerful cryptographic primitive with various applications such as secure multiparty computation, verifiable computation, parallel cryptography, and complexity lower-bounds. Intuitively, randomized encoding $\hat{f}$ of a function $f$ is another function such that $f(x)$ can be recovered from $\hat{f}(x)$, and nothing except for $f(x)$ is leaked from $\hat{f}(x)$. Its quantum version, quantum randomized encoding, has been introduced recently [Brakerski and Yuen, arXiv:2006.01085]. Intuitively, quantum randomized encoding $\hat{F}$ of a quantum operation $F$ is another quantum operation such that, for any quantum state $ρ$, $F(ρ)$ can be recovered from $\hat{F}(ρ)$, and nothing except for $F(ρ)$ is leaked from $\hat{F}(ρ)$. In this paper, we show that if quantum randomized encoding of BB84 state generations is possible with an encoding operation $E$, then a two-round verification of quantum computing is possible with a classical verifier who can additionally do the operation $E$. One of the most important goals in the field of the verification of quantum computing is to construct a verification protocol with a verifier as classical as possible. This result therefore demonstrates a potential application of quantum randomized encoding to the verification of quantum computing: if we can find a good quantum randomized encoding (in terms of the encoding complexity), then we can construct a good verification protocol of quantum computing. We, however, also show that too good quantum randomized encoding is impossible: if quantum randomized encoding with a classical encoding operation is possible, then the no-cloning is violated. We finally consider a natural modification of blind quantum computing protocols in such a way that the server gets the output like quantum randomized encoding. We show that the modified protocol is not secure.
