Related papers: Distillation Protocols that Involve Local Distingu…

We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orientations are unknown. We propose a simple and low-complexity…

We analyse the problem of distillation of entanglement of mixed states in higher dimensional compound systems. Employing the positive maps method [M. Horodecki et al., Phys. Lett. A 223 1 (1996)] we introduce and analyse a criterion of…

Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…

We prove new lower bounds for locally decodable codes and private information retrieval. We show that a 2-query LDC encoding n-bit strings over an l-bit alphabet, where the decoder only uses b bits of each queried position of the codeword,…

We present a unified framework for proving memory lower bounds for multi-pass streaming algorithms that detect planted structures. Planted structures -- such as cliques or bicliques in graphs, and sparse signals in high-dimensional data --…

We consider distillation of secret bits from partially secret noisy correlations P_ABE, shared between two honest parties and an eavesdropper. The most studied distillation scenario consists of joint operations on a large number of copies…

Multipartite quantum states that cannot be uniquely determined by their reduced states of all proper subsets of the parties exhibit some inherit `high-order' correlation. This paper elaborates this issue by giving necessary and sufficient…

Bosonic channels are important in practice as they form a simple model for free-space or fiber-optic communication. Here we consider a single-sender two-receiver pure-loss bosonic broadcast channel and determine the unconstrained capacity…

We consider a variable-length source coding problem subject to local decodability constraints. In particular, we investigate the blocklength scaling behavior attainable by encodings of $r$-sparse binary sequences, under the constraint that…

Quantum theory imposes fundamental limitations to the amount of information that can be carried by any quantum system. On the one hand, Holevo bound rules out the possibility to encode more information in a quantum system than in its…

The performance of quantum classifiers is typically analyzed through global state distinguishability or the trainability of variational models. This study investigates how much class information remains accessible under locality-constrained…

Large-scale quantum-correlated networks could transform technologies ranging from communications and cryptography to computation, metrology, and simulation of novel materials. Critical to achieving such quantum enhancements is distributing…

In this paper, we consider a class of constrained clustering problems of points in $\mathbb{R}^{d}$, where $d$ could be rather high. A common feature of these problems is that their optimal clusterings no longer have the locality property…

While the detection of entanglement has been proved already to be quite a difficult task, experimental quantification of entanglement is even more challenging. In this work, we derive an analytical lower bound for the concurrence of a…

High-fidelity quantum entanglement enables key quantum networking capabilities such as secure communication and distributed quantum computing, but long-distance entanglement distribution is limited by noise and loss. Entanglement…

We provide generalizations of known two-qubit entanglement distillation protocols for arbitrary Hilbert space dimensions. The protocols, which are analogues of the hashing and breeding procedures, are adapted to bipartite quantum states…

Evaluating large language models across many benchmarks is expensive, yet many benchmarks are highly correlated. We formalize the selection of a small, informative subset as submodular maximization under a multivariate Gaussian model.…

Locally accessible information is a useful information-theoretic physical quantity of an ensemble of multiparty quantum states. We find it has properties akin to quantum as well as classical correlations of single multiparty quantum states.…

Quantum channels underlie the dynamics of quantum systems, but in many practical settings it is the channels themselves that require processing. We establish universal limitations on the processing of both quantum states and channels,…

Finding the dense regions of a graph and relations among them is a fundamental problem in network analysis. Core and truss decompositions reveal dense subgraphs with hierarchical relations. The incremental nature of algorithms for computing…