Quantum — 1001 Proofs

Yuriy Aronov

1001 proofs in Post-quantum

Yuriy Aronov

1001 proofs in Quantum Mechanics

Yuriy Aronov

1001 proofs in Quantum Chemistry

Hirotada Kobayashi, Keiji Matsumoto, Tomoyuki Yamakami

This paper introduces quantum ``multiple-Merlin''-Arthur proof systems in which Arthur receives multiple quantum proofs that are unentangled with each other. Although classical multi-proof systems are obviously equivalent to classical single-proof systems (i.e., usual Merlin-Arthur proof systems), it is unclear whether or not quantum multi-proof systems collapse to quantum single-proof systems (i.e., usual quantum Merlin-Arthur proof systems). This paper presents a necessary and sufficient condition under which the number of quantum proofs is reducible to two. It is also proved that, in the case of perfect soundness, using multiple quantum proofs does not increase the power of quantum Merlin-Arthur proof systems.

Dominique Unruh

We motivate, define and construct quantum proofs of knowledge, proofs of knowledge secure against quantum adversaries. Our constructions are based on a new quantum rewinding technique that allows us to extract witnesses in many classical proofs of knowledge. We give criteria under which a classical proof of knowledge is a quantum proof of knowledge. Combining our results with Watrous’ results on quantum zeroknowledge, we show that there are zero-knowledge quantum proofs of knowledge for all languages in NP.

Duong Hieu Phan, Weiqiang Wen, Xingyu Yan +1 more

With the rapid development of quantum computers, proofs of quantumness have recently become an interesting research direction. However, in current schemes for proofs of quantumness, quantum provers face the risk of being maliciously exploited by classical verifiers. Through malicious strategies in interaction with quantum provers, classical verifiers could solve some instances of hard problems that arise from the specific scheme in use. This is due to the lack of formalization that prevents malicious verifiers from extracting useful information in proofs of quantumness. To address this issue, we formalize zero-knowledge proofs of quantumness. Intuitively, the zero-knowledge property necessitates that the information gained by the classical verifier from interactions with the quantum prover should not surpass what can be simulated using a simulated classical prover interacting with the same verifier. As a result, the new zero-knowledge notion can prevent a malicious verifier from exploiting quantum advantage. We find that the classical zero-knowledge proof is sufficient to compile some existing proofs of quantumness schemes into zero-knowledge proofs of quantumness schemes. It appears to be more general to require zero-knowledge proof on the verifier side instead of the prover side. This helps to regulate the verifier's behavior from malicious to be honest-but-curious. As a result, both parties will play not only one role in the proofs of quantumness but also the dual role in the classical zero-knowledge proof. Specifically, Shor's factoring-based scheme and the learning with errors-based scheme in [Brakerski et al., FOCS, 2018] can be transformed into zero-knowledge proofs of quantumness by requiring an extractable non-interactive zero-knowledge argument on the verifier side. Zero-knowledge proofs of quantumness can thus be viewed as an enhanced security notion for proofs of quantumness.