Related papers: Quantum Closeness Testing: A Streaming Algorithm a…
A fundamental problem in statistics and learning theory is to test properties of distributions. We show that quantum computers can solve such problems with significant speed-ups. In particular, we give fast quantum algorithms for testing…
The area of property testing tries to design algorithms that can efficiently handle very large amounts of data: given a large object that either has a certain property or is somehow "far" from having that property, a tester should…
We describe two procedures which, given access to one copy of a quantum state and a sequence of two-outcome measurements, can distinguish between the case that at least one of the measurements accepts the state with high probability, and…
We study the impact of quantum computation on the fundamental problem of testing the property of distributions. In particular, we focus on testing whether two unknown classical distributions are close or far enough, and propose the…
We explore potential quantum speedups for the fundamental problem of testing the properties of closeness and $k$-wise uniformity of probability distributions. Closeness testing is the problem of distinguishing whether two $n$-dimensional…
The task of testing whether two uncharacterized quantum devices behave in the same way is crucial for benchmarking near-term quantum computers and quantum simulators, but has so far remained open for continuous-variable quantum systems. In…
Suppose one has access to oracles generating samples from two unknown probability distributions P and Q on some N-element set. How many samples does one need to test whether the two distributions are close or far from each other in the…
Self-testing is a method of quantum state and measurement estimation that does not rely on assumptions about the inner working of the used devices. Its experimental realization has been limited to sources producing single quantum states so…
In this paper, we study the following question: given a black box performing some unknown quantum measurement on a multi-qudit system, how do we test whether this measurement has certain property or is far away from having this property. We…
We present a novel framework closely linking the areas of property testing and data streaming algorithms in the setting of general graphs. It has been recently shown (Monemizadeh et al. 2017) that for bounded-degree graphs, any…
We present several new examples of speed-ups obtainable by quantum algorithms in the context of property testing. First, motivated by sampling algorithms, we consider probability distributions given in the form of an oracle $f:[n]\to[m]$.…
Quantifying and verifying the control level in preparing a quantum state are central challenges in building quantum devices. The quantum state is characterized from experimental measurements, using a procedure known as tomography, which…
We introduce a protocol addressing the conformance test problem, which consists in determining whether a process under test conforms to a reference one. We consider a process to be characterized by the set of end-product it produces, which…
Quantum state purification is the task of recovering a nearly pure copy of an unknown pure quantum state using multiple noisy copies of the state. This basic task has applications to quantum communication over noisy channels and quantum…
We initiate the systematic study of QMA algorithms in the setting of property testing, to which we refer as QMA proofs of proximity (QMAPs). These are quantum query algorithms that receive explicit access to a sublinear-size untrusted proof…
The goal of self-testing is to characterize an a priori unknown quantum system based solely on measurement statistics, i.e. using an uncharacterized measurement device. Here we develop self-testing methods for quantum prepare-and-measure…
In the context of language recognition, we demonstrate the superiority of streaming property testers against streaming algorithms and property testers, when they are not combined. Initiated by Feigenbaum et al., a streaming property tester…
The fact that quantum mechanics predicts stronger correlations than classical physics is an essential cornerstone of quantum information processing. Indeed, these quantum correlations are a valuable resource for various tasks, such as…
There has been a surge of progress in recent years in developing algorithms for testing and learning quantum states that achieve optimal copy complexity. Unfortunately, they require the use of entangled measurements across many copies of…
We initiate a thorough study of \emph{distributed property testing} -- producing algorithms for the approximation problems of property testing in the CONGEST model. In particular, for the so-called \emph{dense} testing model we emulate…