Physics – Quantum Physics
Scientific paper
2007-02-07
Physics
Quantum Physics
7 pages, 3 figures, uses aaai.sty
Scientific paper
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computing) the nature of the relevant uncertainty is non-classical, and the laws of classical probability theory are superseded by those of quantum mechanics. In this paper we introduce Markovian Entanglement Networks (MEN), a novel class of graphical representations of quantum-mechanical dependencies in the context of such non-classical systems. MEN are the quantum-mechanical analogue of Markovian Networks, a family of undirected graphical representations which, in the classical domain, exploit a notion of conditional independence among subsystems. After defining a notion of conditional independence appropriate to our domain (conditional separability), we prove that the conditional separabilities induced by a quantum-mechanical wave function are effectively reflected in the graphical structure of MEN. Specifically, we show that for any wave function there exists a MEN which is a perfect map of its conditional separabilities. Next, we show how the graphical structure of MEN can be used to effectively classify the pure states of three-qubit systems. We also demonstrate that, in large systems, exploiting conditional independencies may dramatically reduce the computational burden of various inference tasks. In principle, the graph-theoretic representation of conditional independencies afforded by MEN may not only facilitate the classical simulation of quantum systems, but also provide a guide to the efficient design and complexity analysis of quantum algorithms and circuits.
Mura Pierfrancesco La
Swiatczak Lukasz
No associations
LandOfFree
Markovian Entanglement Networks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Markovian Entanglement Networks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Markovian Entanglement Networks will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-219383