4 papers
Bayesian Networks of Density Operators
Steffen Lauritzen, Piotr Zwiernik
We study quantum analogues of Bayesian networks on a directed acyclic graph (DAG), distinguishing two constructions for positive definite density operators on finite-dimensional te…
The Markov Marginal Problem for Density Operators
Steffen Lauritzen, Piotr Zwiernik
We study when local reduced density operators, viewed as quantum marginals, can be assembled into a global quantum state with a prescribed Markov structure. The starting point is a…
Total Variation Convergence Preserves Conditional Independence
Steffen Lauritzen
This note establishes that if a sequence of probability measures converges in total variation to the limiting probability measure , and -algebras $\mathbb{A…
Unifying Markov Properties for Graphical Models
Steffen Lauritzen, Kayvan Sadeghi
Several types of graphs with different conditional independence interpretations --- also known as Markov properties --- have been proposed and used in graphical models. In this pap…