dorsal/arxiv
View SchemaConfiguration-Space Location of the Entanglement between Two Subsystems
| Authors | H. -C. Lin, A. J. Fisher |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0609078 |
| URL | https://arxiv.org/abs/quant-ph/0609078 |
| DOI | 10.1103/PhysRevA.75.032330 |
| Journal | Phys. Rev. A 75, 032330 (2007) |
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 continuous-variable 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 sub-ensemble in which the system is definitely located in the restricted region after the measurement is also pure, and hence its entanglement can be simply characterised 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 find also 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.
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"abstract": "In this paper we address the question: where in configuration space is the\nentanglement between two particles located? We present a thought-experiment,\nequally applicable to discrete or continuous-variable systems, in which one or\nboth parties makes a preliminary measurement of the state with only enough\nresolution to determine whether or not the particle resides in a chosen region,\nbefore attempting to make use of the entanglement. We argue that this provides\nan operational answer to the question of how much entanglement was originally\nlocated within the chosen region. We illustrate the approach in a spin system,\nand also in a pair of coupled harmonic oscillators. Our approach is\nparticularly simple to implement for pure states, since in this case the\nsub-ensemble in which the system is definitely located in the restricted region\nafter the measurement is also pure, and hence its entanglement can be simply\ncharacterised by the entropy of the reduced density operators. For our spin\nexample we present results showing how the entanglement varies as a function of\nthe parameters of the initial state; for the continuous case, we find also how\nit depends on the location and size of the chosen regions. Hence we show that\nthe distribution of entanglement is very different from the distribution of the\nclassical correlations.",
"arxiv_id": "quant-ph/0609078",
"authors": [
"H. -C. Lin",
"A. J. Fisher"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.75.032330",
"journal_ref": "Phys. Rev. A 75, 032330 (2007)",
"title": "Configuration-Space Location of the Entanglement between Two Subsystems",
"url": "https://arxiv.org/abs/quant-ph/0609078"
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