Related papers: Factorization of Quantum Density Matrices Accordin…
We observe an undirected graph $G$ without multiple edges and self-loops, which is to represent a protein-protein interaction (PPI) network. We assume that $G$ evolved under the duplication-mutation with complementarity (DMC) model from a…
We study the entanglement in tripartite quantum systems by using the principal basis matrix representations of density matrices. Using the Schmidt decomposition and local unitary transformation, we first convert the general states to…
Density estimation is a central task in statistics and machine learning. This problem aims to determine the underlying probability density function that best aligns with an observed data set. Some of its applications include statistical…
We present a framework for certifying entanglement properties of quantum states and measurements in line networks. The framework is based on the generalised Choi isomorphism, which can be used to map bipartite states and measurements into…
We introduce with geometric means a density matrix decomposition of a multipartite quantum system of a finite dimension into two density matrices: a separable one, also known as the best separable approximation, and an essentially entangled…
This paper deals with identifiability of undirected dynamical networks with single-integrator node dynamics. We assume that the graph structure of such networks is known, and aim to find graph-theoretic conditions under which the state…
It is a fundamental, but still elusive question whether the schemes based on quantum mechanics, in particular on quantum entanglement, can be used for classical information processing and machine learning. Even partial answer to this…
Randomising networks using a naive `accept-all' edge-swap algorithm is generally biased. Building on recent results for nondirected graphs, we construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities for…
Bayesian inference of Bayesian network structures is often performed by sampling directed acyclic graphs along an appropriately constructed Markov chain. We present two techniques to improve sampling. First, we give an efficient…
We study a certain class of classical one dimensional piecewise linear maps. For these systems we introduce an infinite family of Markov partitions into equal cells. The symbolic dynamics generated by these systems is described by…
We review and generalize the recently introduced framework of entropy vectors for detecting and quantifying genuine multipartite entanglement in high dimensional multicomponent quantum systems. We show that these ideas can be extended to…
One of the classical results concerning quantum channels is the characterization of entanglement-breaking channels [M. Horodecki et al., Rev. Math. Phys 15, 629 (2003)]. We address the question whether there exists a similar…
We use a tensor unfolding technique to prove a new identifiability result for discrete bipartite graphical models, which have a bipartite graph between an observed and a latent layer. This model family includes popular models such as…
We study Bayesian networks based on max-linear structural equations as introduced in Gissibl and Kl\"uppelberg [16] and provide a summary of their independence properties. In particular we emphasize that distributions for such networks are…
We introduce generalized quantum Markov states and generalized d-Markov chains which extend the notion quantum Markov chains on spin systems to that on $C^*$-algebras defined by general graphs. As examples of generalized d-Markov chains, we…
The Kronecker product is an invaluable tool for data-sparse representations of large networks and matrices with countless applications in machine learning, graph theory and numerical linear algebra. In some instances, the sparsity pattern…
Conditional independence models associated with directed acyclic graphs (DAGs) may be characterized in at least three different ways: via a factorization, the global Markov property (given by the d-separation criterion), and the local…
The practical utility of a quantum network depends on its ability to establish entanglement between arbitrary node pairs with quality sufficient to execute entanglement enabled tasks. This capability can be assessed globally, through…
We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…
Learning the directed acyclic graph (DAG) structure of a Bayesian network from observational data is a notoriously difficult problem for which many hardness results are known. In this paper we propose a provably polynomial-time algorithm…