Related papers: Factorization of Quantum Density Matrices Accordin…
We derive a sequence of measures whose corresponding Jacobi matrices have special properties and a general mapping of an open quantum system onto 1D semi infinite chains with only nearest neighbour interactions. Then we proceed to use the…
Entanglement is an essential ingredient for building a quantum network that can have many applications. Understanding how entanglement is distributed in a network is a crucial step to move forward. Here we study the conservation and…
Bayesian networks are a widely-used class of probabilistic graphical models capable of representing symmetric conditional independence between variables of interest using the topology of the underlying graph. For categorical variables, they…
Grid states form a discrete set of mixed quantum states that can be described by graphs. We characterize the entanglement properties of these states and provide methods to evaluate entanglement criteria for grid states in a graphical way.…
We report a scalable hybrid quantum-classical machine learning framework to build Bayesian networks (BN) that captures the conditional dependence and causal relationships of random variables. The generation of a BN consists of finding a…
Graphical models of probabilistic dependencies have been extensively investigated in the context of classical uncertainty. However, in some domains (most notably, in computational physics and quantum computing) the nature of the relevant…
We derive a bound on the ability of a linear optical network to estimate a linear combination of independent phase shifts by using an arbitrary non-classical but unentangled input state, thereby elucidating the quantum resources required to…
We point out that density matrices can only be used to describe quantum states, so the entanglement contained in a density matrix is just quantum entanglement. This means a bipartite state described by a density matrix contains quantum…
Symmetric independence relations are often studied using graphical representations. Ancestral graphs or acyclic directed mixed graphs with $m$-separation provide classes of symmetric graphical independence models that are closed under…
We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…
The quantum density matrix generalises the classical concept of probability distribution to quantum theory. It gives the complete description of a quantum state as well as the observable quantities that can be extracted from it. Its…
In this paper we introduce a nonextensive quantum information theoretic measure which may be defined between any arbitrary number of density matrices, and we analyze its fundamental properties in the spectral graph-theoretic framework.…
We introduce a mapping between graphs and pure quantum bipartite states and show that the associated entanglement entropy conveys non-trivial information about the structure of the graph. Our primary goal is to investigate the family of…
Quantum networks are promising venues for quantum information processing. This motivates the study of the entanglement properties of the particular multipartite quantum states that underpin these structures. In particular, it has been…
Finding hidden layers in complex networks is an important and a non-trivial problem in modern science. We explore the framework of quantum graphs to determine whether concealed parts of a multi-layer system exist and if so then what is…
Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Bayesian networks are a class of graphical models that allow to represent a collection of random variables and their condititional…
We show that every density matrix of an n-particle system prepared by a quantum network of constant depth is asymptotically commuting with the mean-field observables. We introduce certain pairs of hypersurfaces in the space of density…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be…
A causal model is an abstract representation of a physical system as a directed acyclic graph (DAG), where the statistical dependencies are encoded using a graphical criterion called `d-separation'. Recent work by Wood & Spekkens shows that…
We propose an extension of the Contextual Graph Markov Model, a deep and probabilistic machine learning model for graphs, to model the distribution of edge features. Our approach is architectural, as we introduce an additional Bayesian…