Factorization of Quantum Density Matrices According to Bayesian and Markov Networks
| dc.creator | Tucci, Robert R. | |
| dc.date | 2007-01-28 | |
| dc.date.accessioned | 2026-07-07T07:43:43Z | |
| dc.date.available | 2026-07-07T07:43:43Z | |
| dc.description | We show that any quantum density matrix can be represented by a Bayesian network (a directed acyclic graph), and also by a Markov network (an undirected graph). We show that any Bayesian or Markov net that represents a density matrix, is logically equivalent to a set of conditional independencies (symmetries) satisfied by the density matrix. We show that the d-separation theorems of classical Bayesian and Markov networks generalize in a simple and natural way to quantum physics. The quantum d-separation theorems are shown to be closely connected to quantum entanglement. We show that the graphical rules for d-separation can be used to detect pairs of nodes (or of node sets) in a graph that are unentangled. CMI entanglement (a.k.a. squashed entanglement), a measure of entanglement originally discovered by analyzing Bayesian networks, is an important part of the theory of this paper. | |
| dc.description | 48 pages (files: 1 .tex, 1 .sty, 7 .eps) | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0701201 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0701201 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122937 | |
| dc.subject | Quantum Physics | |
| dc.title | Factorization of Quantum Density Matrices According to Bayesian and Markov Networks | |
| dc.type | text |