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

by   Tomoyuki Morimae, et al.

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 f̂ of a function f is another function such that f(x) can be recovered from f̂(x), and nothing except for f(x) is leaked from f̂(x). Its quantum version, quantum randomized encoding, has been introduced recently [Brakerski and Yuen, arXiv:2006.01085]. Intuitively, quantum randomized encoding F̂ of a quantum operation F is another quantum operation such that, for any quantum state ρ, F(ρ) can be recovered from F̂(ρ), and nothing except for F(ρ) is leaked from F̂(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.



There are no comments yet.



Quantum Garbled Circuits

We present a garbling scheme for quantum circuits, thus achieving a deco...

Position-based cryptography: Single-qubit protocol secure against multi-qubit attacks

While it is known that unconditionally secure position-based cryptograph...

Two-message verification of quantum computation

We describe a two-message protocol that enables a purely classical verif...

Classical Verification of Quantum Computations with Efficient Verifier

In this paper, we extend the protocol of classical verification of quant...

Constant-round Blind Classical Verification of Quantum Sampling

In a recent breakthrough, Mahadev constructed a classical verification o...

Private Set Intersection with Delegated Blind Quantum Computing

Private set intersection is an important problem with implications in ma...

Information-theoretically-sound non-interactive classical verification of quantum computing with trusted center

The posthoc verification protocol [J. F. Fitzsimons, M. Hajdušek, and T....
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.