Related papers: A synchronous NPA hierarchy with applications
We introduce a hierarchy of tests satisfied by any probability distribution $P$ that represents the quantum correlations generated in prepare-and-measure (P\&M) quantum chain-shaped networks, assuming only the inner-product information of…
We give a convergent hierarchy of SDP certificates for bounding the spectral gap of local qubit Hamiltonians from below. Our approach is based on the NPA hierarchy applied to a polynomially-sized system of constraints defining the universal…
Characterising the correlations that arise from locally measuring a single part of a joint quantum system is one of the main problems of quantum information theory. The seminal work [M. Navascu\'es et al., New J. Phys. 10, 073013 (2008)],…
An important problem in quantum information theory is that of bounding sets of correlations that arise from making local measurements on entangled states of arbitrary dimension. Currently, the best-known method to tackle this problem is the…
We are interested in the problem of characterizing the correlations that arise when performing local measurements on separate quantum systems. In a previous work [Phys. Rev. Lett. 98, 010401 (2007)], we introduced an infinite hierarchy of…
In this work, we consider the problem of synchronizing two sets of data where the size of the symmetric difference between the sets is small and, in addition, the elements in the symmetric difference are related through the Hamming distance…
We derive a device-independent quantum key distribution protocol based on synchronous correlations and their Bell inequalities. This protocol offers several advantages over other device-independent schemes including symmetry between the two…
We describe a simple and flexible method for implementing semi-definite programming relaxations for bounding the set of quantum correlations. The method relies on obtaining equality constraints from randomly sampled moment matrices and…
For many years, Herlihy's elegant computability based Consensus Hierarchy has been our best explanation of the relative power of various types of multiprocessor synchronization objects when used in deterministic algorithms. However, key to…
Sequence alignment supports numerous tasks in bioinformatics, natural language processing, pattern recognition, social sciences, and others fields. While the alignment of two sequences may be performed swiftly in many applications, the…
Synchronization control in arrays of identical output-coupled continuous-time linear systems is studied. Sufficiency of new conditions for the existence of a synchronizing feedback law are analyzed. It is shown that for neutrally stable…
Finding a provably correct subquadratic synchronization algorithm for many filesystem replicas is one of the main theoretical problems in Operational Transformation (OT) and Conflict-free Replicated Data Types (CRDT) frameworks. Based on…
We investigate the synchronization dynamics in a chain of coupled chaotic maps organized in a single-parent family tree, whose properties can be captured considering each parent node connected to two children, one of which also serves as…
The process of rank aggregation is intimately intertwined with the structure of skew-symmetric matrices. We apply recent advances in the theory and algorithms of matrix completion to skew-symmetric matrices. This combination of ideas…
Accuracy certificates for convex minimization problems allow for online verification of the accuracy of approximate solutions and provide a theoretically valid online stopping criterion. When solving the Lagrange dual problem, accuracy…
Homomorphic encryption has largely been studied in context of public key cryptosystems. But there are applications which inherently would require symmetric keys. We propose a symmetric key encryption scheme with fully homomorphic evaluation…
We study $\textit{sparse singular value certificates}$ for random rectangular matrices. If $M$ is an $n \times d$ matrix with independent Gaussian entries, we give a new family of polynomial-time algorithms which can certify upper bounds on…
In this paper, we propose an approach of the nucleon-pair approximation (NPA), in which the collective nucleon pairs are represented in terms of antisymmetric matrices, and commutations between nucleon pairs are given by using matrix…
We define a novel notion of ``non-backtracking'' matrix associated to any symmetric matrix, and we prove a ``Ihara-Bass'' type formula for it. We use this theory to prove new results on polynomial-time strong refutations of random…
The Balanced-Pairwise-Affinities (BPA) feature transform is designed to upgrade the features of a set of input items to facilitate downstream matching or grouping related tasks. The transformed set encodes a rich representation of high…