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Paper 1

Entanglement-assisted Quantum Codes from Cyclic Codes

Francisco Revson F. Pereira

Year

2019

Journal

arXiv preprint

DOI

arXiv:1911.06384

arXiv

1911.06384

Entanglement-assisted quantum (QUENTA) codes are a subclass of quantum error-correcting codes which use entanglement as a resource. These codes can provide error correction capability higher than the codes derived from the traditional stabilizer formalism. In this paper, it is shown a general method to construct QUENTA codes from cyclic codes. Afterwards, the method is applied to Reed-Solomon codes, BCH codes, and general cyclic codes. We use the Euclidean and Hermitian construction of QUENTA codes. Two families of QUENTA codes are maximal distance separable (MDS), and one is almost MDS or almost near MDS. The comparison of the codes in this paper is mostly based on the quantum Singleton bound.

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Paper 2

Relative entanglement entropy for widely separated regions in curved spacetime

Stefan Hollands, Onirban Islam, Ko Sanders

Year

2017

Journal

arXiv preprint

DOI

arXiv:1711.02039

arXiv

1711.02039

We give an upper bound of the relative entanglement entropy of the ground state of a massive Dirac-Majorana field across two widely separated regions $A$ and $B$ in a static slice of an ultrastatic Lorentzian spacetime. Our bound decays exponentially in $dist (A, B)$, at a rate set by the Compton wavelength and the spatial scalar curvature. The physical interpretation our result is that, on a manifold with positive spatial scalar curvature, one cannot use the entanglement of the vacuum state to teleport one classical bit from $A$ to $B$ if their distance is of the order of the maximum of the curvature radius and the Compton wave length or greater.

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