# Gaussian Genuinely Multipartite Entangled states - 5 and 6 modes (thesis data)

Dataset

## Description

MATLAB files of Covariance matrices and Witnesses for the 5 and 6 mode examples presented in the corresponding thesis (table 6.7 on page 106). Details on how the data was obtained is found in the thesis.

Datqa may be accessed using MATLAB, make sure that the working directory includes the file 'GMEClass.m'.
To get the values use the command:
>> f = matfile('Nordgren2022_5modeData.mat');
fives01222 = f.fives01222
fives01233 = f.fives01233
fives01234 = f.fives01234

The numbers at the end are a way of describing trees.
Each entry corresponds to a vertex. The value corresponds to the other vertex the entry connects to - with zero being a bare vertex.
So the 4-mode linear tree would be 0 1 2 3 (start with a bare A, B connects to A, C connects to B, D connects to C).
The five mode example below 0 1 2 2 2 is the star-shaped (all connected to the middle vertex). For unlabeled trees this is equivalent to 0 1 1 1 1.
In MATLAB one may draw the tree passing a vector of the node connections using the command:
>> treeplot([0 1 2 3 4])

Each fivesXXXXX holds all the info for the graph given by XXXXX. To get the values use (using the first example)
fives01222.c - witness mean
fives01222.g - covariance matrix
fives01222.w - witness
fives01222.s - seed matrix
fives01222.t - tree structure.

You should be able to check that the values are self-coherent with
>> trace(g*w) - 1 - c == 0

Likewise, for N=6 use commands below. (feel free to use other variables different to ff1,etc.)
ff = matfile('Nordgren2022_6modeData.mat');
ff1 = ff.sixes012222
ff2 = ff.sixes012233
ff3 = ff.sixes012333
ff4 = ff.sixes012335
ff5 = ff.sixes012344
ff6 = ff.sixes012345
with the same associated object values as above.
Date made available 4 Aug 2022 University of St Andrews 2021

## Keywords

• quantum information
• entanglement
• genuine multipartite
• ### Hybrid ancilla-based quantum computation and emergent Gaussian multipartite entanglement

Author: Nordgren, V. M., 12 Jun 2023

Supervisor: Korolkova, N. (Supervisor)

Student thesis: Doctoral Thesis (PhD)