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In unitary property testing a quantum algorithm, also known as a tester, is given query access to a black-box unitary and has to decide whether it satisfies some property. We propose a new technique for proving lower bounds on the quantum…
We study two group theoretic problems, GROUP INTERSECTION and DOUBLE COSET MEMBERSHIP, in the setting of black-box groups, where DOUBLE COSET MEMBERSHIP generalizes a set of problems, including GROUP MEMBERSHIP, GROUP FACTORIZATION, and…
In this paper, we present a simple bare-bones solution of a Zero-Knowledge authentication protocol which uses non-commutative algebra and a variation of the generalized symmetric decomposition problem (GSDP) as a one-way function. The…
We consider a type of zero-knowledge protocols that are of interest for their practical applications within networks like the Internet: efficient zero-knowledge arguments of knowledge that remain secure against concurrent man-in-the-middle…
We construct a quantum oracle relative to which $\mathsf{BQP} = \mathsf{QMA}$ but cryptographic pseudorandom quantum states and pseudorandom unitary transformations exist, a counterintuitive result in light of the fact that pseudorandom…
Two of the fundamental no-go theorems of quantum information are the no-cloning theorem (that it is impossible to make copies of general quantum states) and the no-teleportation theorem (the prohibition on telegraphing, or sending quantum…
Since the concern of privacy leakage extremely discourages user participation in sharing data, federated learning has gradually become a promising technique for both academia and industry for achieving collaborative learning without leaking…
This paper shows that, if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hidden-variable theory…
Numerous conceptually important quantum algorithms rely on a black-box device known as an oracle, which is typically difficult to construct without knowing the answer to the problem that the algorithm is intended to solve. A notable example…
Bit commitment schemes are at the basis of modern cryptography. Since information-theoretic security is impossible both in the classical and the quantum regime, we need to look at computationally secure commitment schemes. In this paper, we…
We study the problem of learning an unknown graph provided via an oracle using a quantum algorithm. We consider three query models. In the first model ("OR queries"), the oracle returns whether a given subset of the vertices contains any…
Zero-knowledge proofs (ZKPs) are widely applied in digital economies, such as cryptocurrencies and smart contracts, for establishing trust and ensuring privacy between untrusted parties. However, almost all ZKPs rely on unproven…
We use the powerful tools of counting complexity and generic oracles to help understand the limitations of the complexity of quantum computation. We show several results for the probabilistic quantum class BQP. 1. BQP is low for PP, i.e.,…
Quantum computers are widely believed have an advantage over classical computers, and some have even published some empirical evidence that this is the case. However, these publications do not include a rigorous proof of this advantage,…
A typical oracle problem is finding which software program is installed on a computer, by running the computer and testing its input-output behaviour. The program is randomly chosen from a set of programs known to the problem solver. As…
Zero-Knowledge Proofs (ZKPs) have emerged as an important cryptographic technique allowing one party (prover) to prove the correctness of a statement to some other party (verifier) and nothing else. ZKPs give rise to user's privacy in many…
In this article we give several new results on the complexity of algorithms that learn Boolean functions from quantum queries and quantum examples. Hunziker et al. conjectured that for any class C of Boolean functions, the number of quantum…
We define a new model of quantum learning that we call Predictive Quantum (PQ). This is a quantum analogue of PAC, where during the testing phase the student is only required to answer a polynomial number of testing queries. We demonstrate…
What is the power of polynomial-time quantum computation with access to an NP oracle? In this work, we focus on two fundamental tasks from the study of Boolean satisfiability (SAT) problems: search-to-decision reductions, and approximate…
We show that quantum oracles provide an advantage over classical oracles for answering classical counterfactual questions in causal models, or equivalently, for identifying unknown causal parameters such as distributions over functional…