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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 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.

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 investigate the quantum-secure covert-communication capabilities of lossy thermal-noise bosonic channels, the quantum-mechanical model for many practical channels. We determine the expressions for the covert capacity of these channels: Lno-EA, when Alice and Bob share only a classical secret, and LEA, when they benefit from entanglement assistance. We find that entanglement assistance alters the fundamental scaling law for covert communication.

Quantum information science is an exciting, wide, rapidly progressing, cross-disciplinary field, and that very nature makes it both attractive and hard to enter. In this primer, we first provide answers to the three essential questions that any newcomer needs to know: How is quantum information represented? How is quantum information processed? How is classical information extracted from quantum states?

It is known that quantum resources can allow us to achieve a family of equilibria that can have sometimes a better social welfare, while guaranteeing privacy. We use graph games to propose a way to build non-cooperative games from graph states, and we show how to achieve an unlimited improvement with quantum advice compared to classical advice.