diff --git a/README.md b/README.md index 9ffd9c8..f534f9c 100644 --- a/README.md +++ b/README.md @@ -2,14 +2,23 @@ [![Generic badge](https://img.shields.io/badge/arXiv-2305.04899-.svg)](https://arxiv.org/abs/2305.04899) -Code associated with publication on the determination of mode entanglement in bosonic and fermionic Harmonium in the presence of local super-selection rules. +This repository contains code associated with a publication which describes the determination of mode entanglement in bosonic and fermionic Harmonium in the presence of local super-selection rules. The codebase contains a combination of Mathematica notebooks which were used to analytically calculate integrals corresponding to expectation values of the creation/annihilation operators associated with certain mode combinations in various spin configurations and for various particle numbers/spatial dimensions. N always denotes the number of particles and d the spatial dimension so N4d1 would correspond to a one-dimensional system with 4 particles, m corresponds to the mode index, such that m01 in a mode-mode entangled system would correspond to the modes indexed 0 and 1. This consisted in the bulk of the work and the majority of files are Mathematica notebooks labelled in this fashion. "N-RDO" corresponds to the N particle reduced density operator, the calculation of which is required for the determination of all the desired matrix elements. -In some cases, the relative entropy of entanglement was calculated numerically with Matlab where we resorted to an [optimisation package](https://github.com/markwgirard/relEntropy) for input bipartite matrices. The plots shown in the paper were generated in python and are also shown. +In some cases, the relative entropy of entanglement was calculated numerically with Matlab where we resorted to an [optimisation routine](https://github.com/markwgirard/relEntropy) for input bipartite matrices. The plots shown in the paper were generated in python and are also shown. For suspected errors or suggestions please get in touch with [me.](jan.ernst@physics.ox.ac.uk) + ## Requirements + + + ## References Ernst, J. O., & Tennie, F. (2022). Mode Entanglement in Fermionic and Bosonic Harmonium (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2211.09647