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Quantum phenomena provide computing and information handling paradigms that are clearly different and very likely much more powerful than their classical counterparts. Over the past few years, several governments throughout the world have allocated substantial funding aimed at boosting quantum information science. Much progress has been made on the theoretical side, and experiments have been conducted in which quantum computational operations were executed on a small number of quantum bits.

We study hypergraph clustering in the weighted d-uniform hypergraph stochastic block model (d -WHSBM), where each edge consisting of d nodes from the same community has higher expected weight than the edges consisting of nodes from different communities. We propose a new hypergraph clustering algorithm, called CRTMLE, and provide its performance guarantee under the d -WHSBM for general parameter regimes. We show that the proposed method achieves the order-wise optimal or the best existing results for approximately balanced community sizes.

In this article, we consider a particular data structure consisting of a union of several nested low-rank subspaces with missing data entries. Given the rank of each subspace, we treat the data completion problem, i.e., to estimate the missing entries. Starting from the case of two-dimensional data, i.e., matrices, we show that the union of nested subspaces data structure leads to a structured decomposition U = XY where the factor Y has blocks of zeros that are determined by the rank values.

We develop data processing inequalities that describe how Fisher information from statistical samples can scale with the privacy parameter $\varepsilon $ under local differential privacy constraints. These bounds are valid under general conditions on the distribution of the score of the statistical model, and they elucidate under which conditions the dependence on $\varepsilon $ is linear, quadratic, or exponential.

In this article, we study the problem of non-adaptive group testing, in which one seeks to identify which items are defective given a set of suitably-designed tests whose outcomes indicate whether or not at least one defective item was included in the test. The most widespread recovery criterion seeks to exactly recover the entire defective set, and relaxed criteria such as approximate recovery and list decoding have also been considered.

The problem of distributed testing against independence with variable-length coding is considered when the average and not the maximum communication load is constrained as in previous works. The paper characterizes the optimum type-II error exponent of a single-sensor single-decision center system given a maximum type-I error probability when communication is either over a noise-free rate-R link or over a noisy discrete memoryless channel (DMC) with stop-feedback. Specifically, let E denote the maximum allowed type-I error probability.