dorsal/arxiv
View SchemaTeleportation, Braid Group and Temperley--Lieb Algebra
| Authors | Yong Zhang |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0610148 |
| URL | https://arxiv.org/abs/quant-ph/0610148 |
| DOI | 10.1088/0305-4470/39/37/017 |
| Journal | J.Phys.A39:11599-11622,2006 |
Abstract
We explore algebraic and topological structures underlying the quantum teleportation phenomena by applying the braid group and Temperley--Lieb algebra. We realize the braid teleportation configuration, teleportation swapping and virtual braid representation in the standard description of the teleportation. We devise diagrammatic rules for quantum circuits involving maximally entangled states and apply them to three sorts of descriptions of the teleportation: the transfer operator, quantum measurements and characteristic equations, and further propose the Temperley--Lieb algebra under local unitary transformations to be a mathematical structure underlying the teleportation. We compare our diagrammatical approach with two known recipes to the quantum information flow: the teleportation topology and strongly compact closed category, in order to explain our diagrammatic rules to be a natural diagrammatic language for the teleportation.
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"abstract": "We explore algebraic and topological structures underlying the quantum\nteleportation phenomena by applying the braid group and Temperley--Lieb\nalgebra. We realize the braid teleportation configuration, teleportation\nswapping and virtual braid representation in the standard description of the\nteleportation. We devise diagrammatic rules for quantum circuits involving\nmaximally entangled states and apply them to three sorts of descriptions of the\nteleportation: the transfer operator, quantum measurements and characteristic\nequations, and further propose the Temperley--Lieb algebra under local unitary\ntransformations to be a mathematical structure underlying the teleportation. We\ncompare our diagrammatical approach with two known recipes to the quantum\ninformation flow: the teleportation topology and strongly compact closed\ncategory, in order to explain our diagrammatic rules to be a natural\ndiagrammatic language for the teleportation.",
"arxiv_id": "quant-ph/0610148",
"authors": [
"Yong Zhang"
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"quant-ph",
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"doi": "10.1088/0305-4470/39/37/017",
"journal_ref": "J.Phys.A39:11599-11622,2006",
"title": "Teleportation, Braid Group and Temperley--Lieb Algebra",
"url": "https://arxiv.org/abs/quant-ph/0610148"
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