相关论文: Bounds on entanglement dimensions and quantum grap…

We investigate the entanglement of the ground state in the quantum networks that their nodes are considered as quantum harmonic oscillators. To this aim, the Schmidt numbers and entanglement entropy between two arbitrary partitions of a…

Shared entanglement can significantly amplify classical correlations between systems interacting over a limited quantum channel. A natural avenue is to use entanglement of the same dimension as the channel because this allows for unitary…

Quantum correlation often refers to correlations exhibited by two or more local subsystems under a suitable measurement. These correlations are beyond the framework of classical statistics and the associated classical probability…

Quantum entanglement is a key resource, which grants quantum systems the ability to accomplish tasks that are classically impossible. Here, we apply Feynman's sum-over-histories formalism to interacting bipartite quantum systems and…

We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semi-algebraic) design spaces. We use the moment-sum-of-squares hierarchy of semidefinite programming problems…

Considering pure quantum states, entanglement concentration is the procedure where from $N$ copies of a partially entangled state, a single state with higher entanglement can be obtained. Getting a maximally entangled state is possible for…

We present a technique for reducing the computational requirements by several orders of magnitude in the evaluation of semidefinite relaxations for bounding the set of quantum correlations arising from finite-dimensional Hilbert spaces. The…

Continuous-variable encoding of quantum information in the optical domain has recently yielded large temporal and spectral entangled states instrumental for quantum computing and quantum communication. We introduce a protocol for the…

We study the problem of deterministic approximate counting of matchings and independent sets in graphs of bounded connective constant. More generally, we consider the problem of evaluating the partition functions of the monomer-dimer model…

Polynomial optimization problems are infinite-dimensional, nonconvex, NP-hard, and are often handled in practice with the moment-sums of squares hierarchy of semidefinite programming bounds. We consider problems where the objective function…

We consider the problem of partitioning the node set of a graph into $k$ sets of given sizes in order to \emph{minimize the cut} obtained using (removing) the $k$-th set. If the resulting cut has value $0$, then we have obtained a vertex…

We investigate the entanglement structure of bipartite two-qutrit pure states from both geometric and operational perspectives.Using the eigenvalues of the reduced density matrix, we analyze how symmetric polynomials characterize pairwise…

Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…

Entanglement-based quantum networks exhibit a unique flexibility in the choice of entangled resource states that are then locally manipulated by the nodes to fulfill any request in the network. Furthermore, this manipulation is not uniquely…

In this article we consider the graph alignment problem from the perspective of high-dimensional statistics: we aim to estimate an unknown permutation $\pi^*$ from the observation of two correlated random adjacency matrices $A_1$, $A_2$. We…

We propose a technique to investigate multipartite entanglement in the symmetric subspace. Our approach is to map an $N$-qubit symmetric state onto a bipartite symmetric state of higher local dimension. We show that this mapping preserves…

Entanglement plays an important role in quantum communication, algorithms, and error correction. Schmidt coefficients are correlated to the eigenvalues of the reduced density matrix. These eigenvalues are used in Von Neumann entropy to…

Quantum networks are natural scenarios for the communication of information among distributed parties, and the arena of promising schemes for distributed quantum computation. Measurement-based quantum computing is a prominent example of how…

We study the quantumness of correlations for ensembles of bi- and multi-partite systems and relate it to the task of quantum data hiding. Quantumness is here intended in the sense of minimum average disturbance under local measurements. We…

The notions of bounded expansion and nowhere denseness not only offer robust and general definitions of uniform sparseness of graphs, they also describe the tractability boundary for several important algorithmic questions. In this paper we…