dorsal/arxiv
View SchemaEntanglement measure for the universal classes of fractons
| Authors | Wellington da Cruz, S. Shelly Sharma |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0310064 |
| URL | https://arxiv.org/abs/quant-ph/0310064 |
Abstract
We introduce the notion of entanglement measure for the universal classes of fractons as an entanglement between ocuppation-numbers of fractons in the lowest Landau levels and the rest of the many-body system of particles. This definition came as an entropy of the probability distribution {\it \`a la} Shannon. Fractons are charge-flux systems classified in universal classes of particles or quasiparticles labelled by a fractal or Hausdorff dimension defined within the interval $1 < h < 2$ and associated with the fractal quantum curves of such objects. They carry rational or irrational values of spin and the spin-statistics connection takes place in this fractal approach to the fractional spin particles. We take into account the fractal von Neumann entropy associated with the fractal distribution function which each universal class of fractons satisfies. We consider the fractional quantum Hall effect-FQHE given that fractons can model Hall states. According to our formulation entanglement between occupaton-numbers in this context increases with the universality classes of the quantum Hall transitions considered as fractal sets of dual topological quantum numbers filling factors. We verify that the Hall states have stronger entanglement between ocuppation-numbers and so we can consider this resource for fracton quantum computing.
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"abstract": "We introduce the notion of entanglement measure for the universal classes of\nfractons as an entanglement between ocuppation-numbers of fractons in the\nlowest Landau levels and the rest of the many-body system of particles. This\ndefinition came as an entropy of the probability distribution {\\it \\`a la}\nShannon. Fractons are charge-flux systems classified in universal classes of\nparticles or quasiparticles labelled by a fractal or Hausdorff dimension\ndefined within the interval $1 \u003c h \u003c 2$ and associated with the fractal quantum\ncurves of such objects. They carry rational or irrational values of spin and\nthe spin-statistics connection takes place in this fractal approach to the\nfractional spin particles. We take into account the fractal von Neumann entropy\nassociated with the fractal distribution function which each universal class of\nfractons satisfies. We consider the fractional quantum Hall effect-FQHE given\nthat fractons can model Hall states. According to our formulation entanglement\nbetween occupaton-numbers in this context increases with the universality\nclasses of the quantum Hall transitions considered as fractal sets of dual\ntopological quantum numbers filling factors. We verify that the Hall states\nhave stronger entanglement between ocuppation-numbers and so we can consider\nthis resource for fracton quantum computing.",
"arxiv_id": "quant-ph/0310064",
"authors": [
"Wellington da Cruz",
"S. Shelly Sharma"
],
"categories": [
"quant-ph"
],
"title": "Entanglement measure for the universal classes of fractons",
"url": "https://arxiv.org/abs/quant-ph/0310064"
},
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