Related papers: Oracle Separations Between Quantum and Non-interac…

A non-interactive ZK (NIZK) proof enables verification of NP statements without revealing secrets about them. However, an adversary that obtains a NIZK proof may be able to clone this proof and distribute arbitrarily many copies of it to…

This work investigates the oracle separation between the physically motivated complexity class of noisy quantum circuits, inspired by definitions such as those presented by Chen, Cotler, Huang, and Li (2022). We establish that with a…

We examine the power of statistical zero knowledge proofs (captured by the complexity class SZK) and their variants. First, we give the strongest known relativized evidence that SZK contains hard problems, by exhibiting an oracle relative…

This paper investigates the power of quantum statistical zero knowledge interactive proof systems in the relativized setting. We prove the existence of an oracle relative to which quantum statistical zero-knowledge does not contain UP…

Zero-knowledge proof (ZKP) is a fundamental cryptographic primitive that allows a prover to convince a verifier of the validity of a statement without leaking any further information. As an efficient variant of ZKP, non-interactive…

A foundational question in quantum computational complexity asks how much more useful a quantum state can be in a given task than a comparable, classical string. Aaronson and Kuperberg showed such a separation in the presence of a quantum…

This paper studies the complexity classes QZK and HVQZK of problems having a quantum computational zero-knowledge proof system and an honest-verifier quantum computational zero-knowledge proof system, respectively. The results proved in…

We initiate the study of non-interactive zero-knowledge (NIZK) arguments for languages in QMA. Our first main result is the following: if Learning With Errors (LWE) is hard for quantum computers, then any language in QMA has an NIZK…

Theoretical computer scientists have been debating the role of oracles since the 1970's. This paper illustrates both that oracles can give us nontrivial insights about the barrier problems in circuit complexity, and that they need not…

We show the following hold, unconditionally unless otherwise stated, relative to a random oracle: - There are NP search problems solvable by quantum polynomial-time machines but not classical probabilistic polynomial-time machines. - There…

The relationship between BQP and PH has been an open problem since the earliest days of quantum computing. We present evidence that quantum computers can solve problems outside the entire polynomial hierarchy, by relating this question to…

This paper proves that several interactive proof systems are zero-knowledge against quantum attacks. This includes a few well-known classical zero-knowledge proof systems as well as quantum interactive proof systems for the complexity class…

Zero-Knowledge (ZK) protocols have been intensely studied due to their fundamental importance and versatility. However, quantum information's inherent differences significantly alter the landscape, necessitating a re-examination of ZK…

A conjecture of Jozsa (arXiv:quant-ph/0508124) states that any polynomial-time quantum computation can be simulated by polylogarithmic-depth quantum computation interleaved with polynomial-depth classical computation. Separately, Aaronson…

We study the notion of zero-knowledge secure against quantum polynomial-time verifiers (referred to as quantum zero-knowledge) in the concurrent composition setting. Despite being extensively studied in the classical setting, concurrent…

In this work we consider the interplay between multiprover interactive proofs, quantum entanglement, and zero knowledge proofs - notions that are central pillars of complexity theory, quantum information and cryptography. In particular, we…

We present the first constructions of single-prover proof systems that achieve perfect zero knowledge (PZK) for languages beyond NP, under no intractability assumptions: 1. The complexity class #P has PZK proofs in the model of Interactive…

We explore the space "just above" BQP by defining a complexity class PDQP (Product Dynamical Quantum Polynomial time) which is larger than BQP but does not contain NP relative to an oracle. The class is defined by imagining that quantum…

In recent years, the quantum oracle model introduced by Aaronson and Kuperberg (2007) has found a lot of use in showing oracle separations between complexity classes and cryptographic primitives. It is generally assumed that proof…

We study the quantum-classical polynomial hierarchy, QCPH, which is the class of languages solvable by a constant number of alternating classical quantifiers followed by a quantum verifier. Our main result is that QCPH is infinite relative…