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Entanglement Theory Quantum Correlations

Quantum Teleportation and Super-dense Coding in Operator Algebras

arXiv
Authors: Li Gao, Samuel J. Harris, Marius Junge

Year

2017

Paper ID

7593

Status

Preprint

Abstract Read

~2 min

Abstract Words

145

Citations

N/A

Abstract

Let mathcal{B}d be the unital C^*-algebra generated by the elements ujk, 0 le i, j le d-1, satisfying the relations that \[uj,k\] is a unitary operator, and let C^*\(mathbb{F}d2\) be the full group C^*-algebra of free group of d2 generators. Based on the idea of teleportation and super-dense coding in quantum information theory, we exhibit the two *-isomorphisms Md\(C^*(mathbb{F}d2\))cong mathcal{B}drtimes mathbb{Z}drtimes mathbb{Z}d and Md\(mathcal{B}d\)cong C^*\(mathbb{F}d2\)rtimes mathbb{Z}drtimes mathbb{Z}d, for certain actions of mathbb{Z}d. As an application, we show that for any d,mge 2 with (d,m)neq (2,2), the matrix-valued generalization of the (tensor product) quantum correlation set of d inputs and m outputs is not closed.

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  • This paper contributes to the Entanglement Theory & Quantum Correlations research area in the Quantum Articles archive.
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  • Let mathcalBd be the unital C^*-algebra generated by the elements ujk, 0 le i, j le d-1, satisfying the relations that [uj,k] is a unitary operator, and let C^*(mathbbFd^2) be...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1709.02785 [2] arXiv https://arxiv.org/abs/1709.02785 [3] Publisher https://arxiv.org/abs/1709.02785

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