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Paper 1

Changing the Local-Dimension of an Entanglement-Assisted Stabilizer Code Removes Entanglement Need

Lane G. Gunderman

Year

2020

Journal

arXiv preprint

DOI

arXiv:2012.13395

arXiv

2012.13395

Having protected quantum information is essential to perform quantum computations. One possibility is to reduce the number of particles needing to be protected from noise and instead use systems with more states, so called qudit quantum computers. In this paper we show that codes for these systems can be derived from already known codes, and in particular this procedure removes the need for shared entanglement in entanglement-assisted quantum error-correcting codes, which is a result which could prove to be useful for fault-tolerant qudit, and even qubit, quantum computers.

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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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