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Home / Proceedings / Papers from the 2007 AAAI Spring Symposium

Markov Entanglement Networks

March 14, 2023

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Authors

Pierfrancesco La Mura

Lukasz Swiatczak

DOI:


Abstract:

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computing) the nature of the relevant uncertainty is non-classical, and the laws of classical probability theory are superseded by those of quantum mechanics.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 Markov 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.

Topics: Spring

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Pierfrancesco La Mura||Lukasz Swiatczak Markov Entanglement Networks Papers from the 2007 AAAI Spring Symposium (2007) .

Pierfrancesco La Mura||Lukasz Swiatczak Markov Entanglement Networks Spring 2007, .

Pierfrancesco La Mura||Lukasz Swiatczak (2007). Markov Entanglement Networks. Papers from the 2007 AAAI Spring Symposium, .

Pierfrancesco La Mura||Lukasz Swiatczak. Markov Entanglement Networks. Papers from the 2007 AAAI Spring Symposium 2007 p..

Pierfrancesco La Mura||Lukasz Swiatczak. 2007. Markov Entanglement Networks. "Papers from the 2007 AAAI Spring Symposium". .

Pierfrancesco La Mura||Lukasz Swiatczak. (2007) "Markov Entanglement Networks", Papers from the 2007 AAAI Spring Symposium, p.

Pierfrancesco La Mura||Lukasz Swiatczak, "Markov Entanglement Networks", Spring, p., 2007.

Pierfrancesco La Mura||Lukasz Swiatczak. "Markov Entanglement Networks". Papers from the 2007 AAAI Spring Symposium, 2007, p..

Pierfrancesco La Mura||Lukasz Swiatczak. "Markov Entanglement Networks". Papers from the 2007 AAAI Spring Symposium, (2007): .

Pierfrancesco La Mura||Lukasz Swiatczak. Markov Entanglement Networks. Spring[Internet]. 2007[cited 2023]; .


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