dorsal/arxiv
View SchemaBrownian Entanglement
| Authors | A. E. Allahverdyan, A. Khrennikov, Th. M. Nieuwenhuizen |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0412132 |
| URL | https://arxiv.org/abs/quant-ph/0412132 |
| DOI | 10.1103/PhysRevA.72.032102 |
Abstract
We show that for two classical brownian particles there exists an analog of continuous-variable quantum entanglement: The common probability distribution of the two coordinates and the corresponding coarse-grained velocities cannot be prepared via mixing of any factorized distributions referring to the two particles in separate. This is possible for particles which interacted in the past, but do not interact in the present. Three factors are crucial for the effect: 1) separation of time-scales of coordinate and momentum which motivates the definition of coarse-grained velocities; 2) the resulting uncertainty relations between the coordinate of the brownian particle and the change of its coarse-grained velocity; 3) the fact that the coarse-grained velocity, though pertaining to a single brownian particle, is defined on a common context of two particles. The brownian entanglement is a consequence of a coarse-grained description and disappears for a finer resolution of the brownian motion. We discuss possibilities of its experimental realizations in examples of macroscopic brownian motion.
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"abstract": "We show that for two classical brownian particles there exists an analog of\ncontinuous-variable quantum entanglement: The common probability distribution\nof the two coordinates and the corresponding coarse-grained velocities cannot\nbe prepared via mixing of any factorized distributions referring to the two\nparticles in separate. This is possible for particles which interacted in the\npast, but do not interact in the present. Three factors are crucial for the\neffect: 1) separation of time-scales of coordinate and momentum which motivates\nthe definition of coarse-grained velocities; 2) the resulting uncertainty\nrelations between the coordinate of the brownian particle and the change of its\ncoarse-grained velocity; 3) the fact that the coarse-grained velocity, though\npertaining to a single brownian particle, is defined on a common context of two\nparticles. The brownian entanglement is a consequence of a coarse-grained\ndescription and disappears for a finer resolution of the brownian motion. We\ndiscuss possibilities of its experimental realizations in examples of\nmacroscopic brownian motion.",
"arxiv_id": "quant-ph/0412132",
"authors": [
"A. E. Allahverdyan",
"A. Khrennikov",
"Th. M. Nieuwenhuizen"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech"
],
"doi": "10.1103/PhysRevA.72.032102",
"title": "Brownian Entanglement",
"url": "https://arxiv.org/abs/quant-ph/0412132"
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