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This folder contains a small python-module that allows you to discover multi-partite quantum-correlations. It was created as a research project for the lecture "Quantum Computation and Communication" given by Stephanie Wehner 2015 at TU Delft.

Quantum Monogamy is a concept from Quantum Information theory. It describes the relation of different parties that may share (entangled) quantum systems. In particular, it can be shown that if two parties, Alice and Bob, share a maximally entangled state (e.g.: EPR-pair), there can be no third party (Charlie) be correlated with either Alice's or Bob's subsystem. Alice and Bob have stablished a monogamous correlation with each other, that limits the access on information for Charlie. However, if the correlation between Alice and Bob is not perfect but subject to noise, Charlie might share state information with Alice and could gain information about measurement outcomes between Alice and Bob.

In order to design robust quantum cryptographic protocols it is of high importance to investigate to what extent quantum states can be correlated between multiple parties.

The module is written in Python3. It depends on NumPy and CVXPY. If you want to use it, you first have to set up a working python3 environment with CVXPY on your system. Installation instructions are found here.

Once your python-environment runs CVXPY, clone the github-repository. If you start a python-shell in the cloned folder (recommended: IPython) you will be able to import and access the module for example by

import monogamy as mg

The interface of monogamy is documented in the examples below.

The following IPython-notebooks illustrate how to use the module. Once you downloaded the IPython-notebooks, you can experiment with them locally and change some values to see what happens.

• Construction of global states

• Usage of the API

As a research project, the module was supposed to be used to analyse a family of quantum states called Werner States. The following IPython-notebook summarizes the task and the obtained results, using the monogamy module.

• Werner State monogamy

• All values that can be used in the density matrices are limited to reals. Complex numbers are no valid inputs and resulting global states will never contain complex numbers as well.
• For larger systems (for example more than 5 qubits), the computational time for finding global states increases as highly constrained optimization problems on large matrices need to be solved.

If you are using this module or like it, let me know.

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.