Related papers: Oracle Separations Between Quantum and Non-interac…
Zero-knowledge proof (ZKP) systems have surged attention and held a fundamental role in contemporary cryptography. Zero-knowledge succinct non-interactive argument of knowledge (zk-SNARK) protocols dominate the ZKP usage, implemented…
In this paper, we introduce a new quantum query lower bound framework. It is inspired by Zhandry's compressed oracle technique, but it also subsumes the polynomial method as a special case. Compared to Zhandry's technique, our approach has…
Any capacity-limited observer induces a canonical quotient on its environment: two situations that no bounded agent can distinguish are, for that agent, the same. We formalise this for finite POMDPs. A fixed probe family of finite-state…
While powerful tools have been developed to analyze quantum query complexity, there are still many natural problems that do not fit neatly into the black box model of oracles. We create a new model that allows multiple oracles with…
We consider a generalization of the standard oracle model in which the oracle acts on the target with a permutation selected according to internal random coins. We describe several problems that are impossible to solve classically but can…
We construct a constant-round zero-knowledge classical argument for NP secure against quantum attacks. We assume the existence of Quantum Fully-Homomorphic Encryption and other standard primitives, known based on the Learning with Errors…
Query complexity is a common tool for comparing quantum and classical computation, and it has produced many examples of how quantum algorithms differ from classical ones. Here we investigate in detail the role that oracles play for the…
Foundational results in theoretical computer science have established that everything provable, is provable in zero knowledge. However, this assertion fundamentally assumes a classical interpretation of computation and many interesting…
We identify a formal connection between physical problems related to the detection of separable (unentangled) quantum states and complexity classes in theoretical computer science. In particular, we show that to nearly every quantum…
We show that for every polynomial q* there exist polynomial-size, constant-query, non-adaptive PCPs for NP which are perfect zero knowledge against (adaptive) adversaries making at most q* queries to the proof. In addition, we construct…
We obtain the strongest separation between quantum and classical query complexity known to date -- specifically, we define a black-box problem that requires exponentially many queries in the classical bounded-error case, but can be solved…
We construct an oracle relative to which $\mathrm{NP} = \mathrm{PSPACE}$, but $\mathrm{UP}$ has no many-one complete sets. This combines the properties of an oracle by Hartmanis and Hemachandra [HH88] and one by Ogiwara and Hemachandra…
Zero-knowledge succinct non-interactive argument of knowledge (zkSNARK) allows a party, known as the prover, to convince another party, known as the verifier, that he knows a private value $v$, without revealing it, such that $F(u,v)=y$ for…
Zero-knowledge and multi-prover systems are both central notions in classical and quantum complexity theory. There is, however, little research in quantum multi-prover zero-knowledge systems. This paper studies complexity-theoretical…
Recently a great deal of attention has focused on quantum computation following a sequence of results suggesting that quantum computers are more powerful than classical probabilistic computers. Following Shor's result that factoring and the…
We show a superpolynomial oracle separation between the power of adiabatic quantum computation with no sign problem and the power of classical computation.
We construct a classically verifiable succinct interactive argument for quantum computation (BQP) with communication complexity and verifier runtime that are poly-logarithmic in the runtime of the BQP computation (and polynomial in the…
Bennett and Gill (1981) showed that P^A != NP^A != coNP^A for a random oracle A, with probability 1. We investigate whether this result extends to individual polynomial-time random oracles. We consider two notions of random oracles:…
We investigate the connection between interference and computational power within the operationally defined framework of generalised probabilistic theories. To compare the computational abilities of different theories within this framework…
The empirical risk minimization (ERM) principle has been highly impactful in machine learning, leading both to near-optimal theoretical guarantees for ERM-based learning algorithms as well as driving many of the recent empirical successes…