Related papers: The Power of Unentanglement
The k-local Hamiltonian problem is a natural complete problem for the complexity class QMA, the quantum analog of NP. It is similar in spirit to MAX-k-SAT, which is NP-complete for k<=2. It was known that the problem is QMA-complete for any…
It is shown that with the use of entanglement a specific two party communication task can be done with a systematically smaller expected error than any possible classical protocol could do. The example utilises the very tight correlation…
Quantum computing is an information processing paradigm that uses quantum-mechanical properties to speedup computationally hard problems. Although promising, existing gate-based quantum computers consist of only a few dozen qubits and are…
We study the long-standing open question on the power of unique witnesses in quantum protocols, which asks if $\textsf{UniqueQMA}$, a variant of $\textsf{QMA}$ whose accepting witness space is 1-dimensional, contains $\mathsf{QMA}$ under…
In computer science, many search problems are reducible to decision problems, which implies that finding a solution is as hard as deciding whether a solution exists. A quantum analogue of search-to-decision reductions would be to ask…
We introduce the reinforcement quantum annealing (RQA) scheme in which an intelligent agent interacts with a quantum annealer that plays the stochastic environment role of learning automata and tries to iteratively find better Ising…
Coherently manipulating multipartite quantum correlations leads to remarkable advantages in quantum information processing. A fundamental question is whether such quantum advantages persist only by exploiting multipartite correlations, such…
We study a model where two opposing provers debate over the membership status of a given string in a language, trying to convince a weak verifier whose coins are visible to all. We show that the incorporation of just two qubits to an…
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…
We study quantum algorithms that are given access to trusted and untrusted quantum witnesses. We establish strong limitations of such algorithms, via new techniques based on Laurent polynomials (i.e., polynomials with positive and negative…
The Quantum Satisfiability problem (QSAT) is the generalization of the canonical NP-complete problem - Boolean Satisfiability. (k,s)-QSAT is the following variant of the problem: given a set of projectors of rank 1, acting non-trivially on…
In known constructions of classical zero-knowledge protocols for NP, either of zero-knowledge or soundness holds only against computationally bounded adversaries. Indeed, achieving both statistical zero-knowledge and statistical soundness…
We prove several new results concerning the pure quantum polynomial hierarchy (pureQPH). First, we show that QMA(2) is contained in pureQSigma2, that is, two unentangled existential provers can be simulated by competing existential and…
The universality of quantum theory has been questioned ever since it was proposed. Key to this long-unsolved question is to test whether a given physical system has non-classical features. Here we connect recently proposed witnesses of…
We investigate two resources whose effects on quantum interactive proofs remain poorly understood: the promise of unentanglement, and the verifier's ability to condition on an intermediate measurement, which we call post-measurement…
Quantum entanglement is a key enabling ingredient in diverse applications. However, the presence of unwanted adversarial entanglement also poses challenges in many applications. In this paper, we explore methods to "break" quantum…
Prior work has established that all problems in NP admit classical zero-knowledge proof systems, and under reasonable hardness assumptions for quantum computations, these proof systems can be made secure against quantum attacks. We prove a…
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…
Entanglement lies at the core of quantum algorithms designed to solve problems that are intractable by classical approaches. One such algorithm, quantum annealing (QA), provides a promising path to a practical quantum processor. We have…
In order to assess whether quantum resources can provide an advantage over classical computation, it is necessary to characterize and benchmark the non-classical properties of quantum algorithms in a practical manner. In this paper, we show…