Configurationspace location of the entanglement between two subsystems
Abstract
In this paper we address the question: where in configuration space is the entanglement between two particles located? We present a thought experiment, equally applicable to discrete or continuousvariable systems, in which one or both parties makes a preliminary measurement of the state with only enough resolution to determine whether or not the particle resides in a chosen region, before attempting to make use of the entanglement. We argue that this provides an operational answer to the question of how much entanglement was originally located within the chosen region. We illustrate the approach in a spin system, and also in a pair of coupled harmonic oscillators. Our approach is particularly simple to implement for pure states, since in this case the subensemble in which the system is definitely located in the restricted region after the measurement is also pure, and hence its entanglement can be simply characterized by the entropy of the reduced density operators. For our spin example we present results showing how the entanglement varies as a function of the parameters of the initial state; for the continuous case, we also find how it depends on the location and size of the chosen regions. Hence we show thatmore »
 Authors:
 UCL Department of Physics and Astronomy and London Centre for Nanotechnology, University College London, Gower Street, London WC1E 6BT (United Kingdom)
 Publication Date:
 OSTI Identifier:
 20982276
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.75.032330; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONFIGURATION; CORRELATIONS; DENSITY; DISTRIBUTION; ENTROPY; HARMONIC OSCILLATORS; MATHEMATICAL OPERATORS; PARTICLE INTERACTIONS; PARTICLES; QUANTUM ENTANGLEMENT; RESOLUTION; SPIN
Citation Formats
Lin, H.C., and Fisher, A. J. Configurationspace location of the entanglement between two subsystems. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.032330.
Lin, H.C., & Fisher, A. J. Configurationspace location of the entanglement between two subsystems. United States. doi:10.1103/PHYSREVA.75.032330.
Lin, H.C., and Fisher, A. J. Thu .
"Configurationspace location of the entanglement between two subsystems". United States.
doi:10.1103/PHYSREVA.75.032330.
@article{osti_20982276,
title = {Configurationspace location of the entanglement between two subsystems},
author = {Lin, H.C. and Fisher, A. J.},
abstractNote = {In this paper we address the question: where in configuration space is the entanglement between two particles located? We present a thought experiment, equally applicable to discrete or continuousvariable systems, in which one or both parties makes a preliminary measurement of the state with only enough resolution to determine whether or not the particle resides in a chosen region, before attempting to make use of the entanglement. We argue that this provides an operational answer to the question of how much entanglement was originally located within the chosen region. We illustrate the approach in a spin system, and also in a pair of coupled harmonic oscillators. Our approach is particularly simple to implement for pure states, since in this case the subensemble in which the system is definitely located in the restricted region after the measurement is also pure, and hence its entanglement can be simply characterized by the entropy of the reduced density operators. For our spin example we present results showing how the entanglement varies as a function of the parameters of the initial state; for the continuous case, we also find how it depends on the location and size of the chosen regions. Hence we show that the distribution of entanglement is very different from the distribution of the classical correlations.},
doi = {10.1103/PHYSREVA.75.032330},
journal = {Physical Review. A},
number = 3,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}

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