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A set of MATLAB scripts for computing bounds on monogamy of entanglement games
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README.md

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)

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