Related papers: Distillation Protocols that Involve Local Distingu…
In this paper, we consider the problem of subspace clustering in presence of contiguous noise, occlusion and disguise. We argue that self-expressive representation of data in current state-of-the-art approaches is severely sensitive to…
We develop new techniques for proving lower bounds on the least singular value of random matrices with limited randomness. The matrices we consider have entries that are given by polynomials of a few underlying base random variables. This…
Computing localizable entanglement for noisy many-particle quantum states is difficult due to the optimization over all possible sets of local projection measurements. Therefore, it is crucial to develop lower bounds, which can provide…
We introduce a local order metric (LOM) that measures the degree of order in the neighborhood of an atomic or molecular site in a condensed medium. The LOM maximizes the overlap between the spatial distribution of sites belonging to that…
Nonlocal correlations are a central feature of quantum theory, and understanding why quantum theory has a limited amount of nonlocality is a fundamental problem. Since nonlocality also has technological applications, e.g., for…
We give lower bounds on the communication complexity required to solve several computational problems in a distributed-memory parallel machine, namely standard matrix multiplication, stencil computations, comparison sorting, and the Fast…
Clustering is a pivotal challenge in unsupervised machine learning and is often investigated through the lens of mixture models. The optimal error rate for recovering cluster labels in Gaussian and sub-Gaussian mixture models involves ad…
The decode-forward achievable region is studied for general networks. The region is subject to a fundamental tension in which nodes individually benefit at the expense of others. The complexity of the region depends on all the ways of…
A least squares semi-supervised local clustering algorithm based on the idea of compressed sensing is proposed to extract clusters from a graph with known adjacency matrix. The algorithm is based on a two-stage approach similar to the one…
Hierarchical Clustering is a popular unsupervised machine learning method with decades of history and numerous applications. We initiate the study of differentially private approximation algorithms for hierarchical clustering under the…
Community detection is one of the most investigated problems in the field of complex networks. Although several methods were proposed, there is still no precise definition of communities. As a step towards a definition, I highlight two…
We establish optimal Statistical Query (SQ) lower bounds for robustly learning certain families of discrete high-dimensional distributions. In particular, we show that no efficient SQ algorithm with access to an $\epsilon$-corrupted binary…
In the topic of perfect local distinguishability of orthogonal multipartite quantum states, most results obtained so far pertain to bipartite systems whose subsystems are of specific dimensions. In contrast very few results for bipartite…
Hypergraphical sources are a natural class of sources for secret key generation, within which different subsets of terminals sharing secrets are allowed to discuss publicly in order to agree upon a global secret key. While their secrecy…
Distributed inner product estimation (DIPE) is a fundamental task in quantum information, aiming to estimate the inner product between two unknown quantum states prepared on distributed quantum platforms. Existing rigorous sample complexity…
We analyze the security of quantum cryptography schemes for $d$-level systems using 2 or $d+1$ maximally conjugated bases, under individual eavesdropping attacks based on cloning machines and measurement after the basis reconciliation. We…
Bipartite quantum interactions have applications in a number of different areas of quantum physics, reaching from fundamental areas such as quantum thermodynamics and the theory of quantum measurements to other applications such as quantum…
Quantum state discrimination is an important problem in many information processing tasks. In this work we are concerned with finding its best possible sample complexity when the states are preprocessed by a quantum channel that is required…
An information-theoretic upper bound on the generalization error of supervised learning algorithms is derived. The bound is constructed in terms of the mutual information between each individual training sample and the output of the…
We consider the discrimination of two-party quantum states and provide a quantum data-hiding scheme using two-qubit separable states. We first provide a bound on the optimal local discrimination of two-party quantum states, and establish a…