https://github.com/vprusso/monogamy-of-entanglement-games
A set of MATLAB scripts for computing bounds on monogamy of entanglement games
https://github.com/vprusso/monogamy-of-entanglement-games
Last synced: 6 months ago
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A set of MATLAB scripts for computing bounds on monogamy of entanglement games
- Host: GitHub
- URL: https://github.com/vprusso/monogamy-of-entanglement-games
- Owner: vprusso
- License: mit
- Created: 2015-09-24T20:26:35.000Z (about 10 years ago)
- Default Branch: master
- Last Pushed: 2015-10-13T17:33:44.000Z (almost 10 years ago)
- Last Synced: 2025-01-28T20:42:18.701Z (8 months ago)
- Language: Matlab
- Size: 124 KB
- Stars: 0
- Watchers: 2
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# MoE
## Version 0.0.1 - 25 September 2015
MoE is a set of MATLAB scripts that supplement the results of the article [2].
To run in MATLAB, add the ```/src/``` directory (including all sub-directories) to your current working directory.
---
MoE is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
MoE is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
---
## Dependencies
In order to run these scripts in MATLAB, you must also have CVX [3] and QETLAB [4] downloaded and added to your ```/src/``` directory.
## Description
This set of scripts allows one to bound the quantum game values for monogamy of entanglement games.
## Use
The purpose of these scripts are to provide a way to compute upper and lower bounds on a specific type of extended nonlocal game called
monogamy-of-entanglement games. These games are defined in terms of a set of measurements for the referee to be performed on its system.
Let's take an example (which is baed on the BB84MonogamyGame in ```src/examples/BB84MonogamyGame.m```. Our choice of basis for this example
will be the BB84 basis, i.e. {|0><0|, |1><1|} and {|+><+|, |-><-|}.
```
e0 = [1;0]; e1 = [0;1]; ep = [1;1]/sqrt(2); em = [1;-1]/sqrt(2);
psi0 = e0*e0'; psi1 = e1*e1'; psip = ep*ep'; psim = em*em';
```
So we have that ```psi0``` = |0><0|, ```psi1``` = |1><1|, ```psip``` = |+><+|, and ```psim``` = |-><-|. We store these elements into a cell array
that represents the measurements of the referee as
```
R{1} = {psi0,psi1}; R{2} = {psip,psim};
```
We may then put this into our functions that compute upper and lower bounds on a monogamy-of-entanglement game defined by these measurements:
```
ub = MonogamyGameValueUB(R,1,1);
lb = MonogamyGameValueLB(R,1,1);
```
More information on the BB84 game can be found in references [1] and [2], and more information on our bounding techniques can be found in [2].
## Examples
### BB84 Monogamy Game
Running the script: ```examples/BB84MonogamyGame.m``` computes the upper and lower bounds for the BB84 monogamy game [1] using the techniques from [2].
### Mutually Unbiased Basis Monogamy Game
Running the script: ```examples/MUB_4_3_MonogamyGame.m``` illustrates a monogamy game defined by a set of mutually unbiased bases consisting of 4-inputs and 3-outputs
where the players benefit from using entanglement as described in [2].
### References:
[1] "A monogamy of entanglement game with applications to device independent
quantum cryptography" - M. Tomamichel, S. Fehr, J. Kaniewski, S. Wehner.
(arxiv:1210.4359)
[2] "Extended nonlocal games and monogamy-of-entanglement games" - N. Johnston,
R. Mittal, V. Russo, J. Watrous. (arxiv:1510.02083)
[3] CVX - (http://cvxr.com/cvx/)
[4] QETLAB v0.8 - (http://qetlab.com)