# toqito: Theory of Quantum Information Toolkit
The `toqito` package is an open-source Python library for studying various
objects in quantum information, namely, states, channels, and measurements.
Specifically, `toqito` focuses on providing numerical tools to study problems
about entanglement theory, nonlocal games, matrix analysis, and other
aspects of quantum information that are often associated with computer science.
`toqito` aims to fill the needs of quantum information researchers who want
numerical and computational tools for manipulating quantum states,
measurements, and channels. It can also be used as a tool to enhance the
experience of students and instructors in classes about quantum
information.
## Getting Started
toqito is available via [PyPi](https://pypi.org/project/toqito/) for Linux, and macOS, with support for Python 3.10 to 3.12.
```console
(venv) $ pip install toqito
```
The following code gives an example on the usage:
```python
# Calculate the classical and quantum value of the CHSH game.
import numpy as np
from toqito.nonlocal_games.xor_game import XORGame
# The probability matrix.
prob_mat = np.array([[1/4, 1/4], [1/4, 1/4]])
# The predicate matrix.
pred_mat = np.array([[0, 0], [0, 1]])
# Define CHSH game from matrices.
chsh = XORGame(prob_mat, pred_mat)
chsh.classical_value()
# 0.75
chsh.quantum_value()
# 0.8535533
```
**Detailed documentation on all available methods, options, and input formats is available at [ReadTheDocs](https://toqito.readthedocs.io/en/latest/).**
## Using
Full documentation along with specific examples and tutorials are provided here:
[https://toqito.readthedocs.io/](https://toqito.readthedocs.io/).
More information can also be found on the following
[toqito homepage](https://vprusso.github.io/toqito/).
Chat with us in our `toqito` channel on [Discord](http://discord.unitary.fund/).
## Testing
The `pytest` module is used for testing. To run the suite of tests for `toqito`,
run the following command in the root directory of this project.
```
pytest --cov-report term-missing --cov=toqito
```
## Citing
You can cite `toqito` using the following DOI:
10.5281/zenodo.4743211
If you are using the `toqito` software package in research work, please include
an explicit mention of `toqito` in your publication. Something along the lines
of:
```
To solve problem "X" we used `toqito`; a package for studying certain
aspects of quantum information.
```
A BibTeX entry that you can use to cite `toqito` is provided here:
```bib
@misc{toqito,
author = {Vincent Russo},
title = {toqito: A {P}ython toolkit for quantum information, version 1.0.0},
howpublished = {\url{https://github.com/vprusso/toqito}},
month = May,
year = 2021,
doi = {10.5281/zenodo.4743211}
}
```
## References
The `toqito` project has been used or referenced in the following works:
- [](https://arxiv.org/abs/2406.13430) Bandyopadhyay, Somshubhro and Russo, Vincent
"Distinguishing a maximally entangled basis using LOCC and shared entanglement", (2024).
- [](https://arxiv.org/abs/2307.02551) Tavakoli, Armin and Pozas-Kerstjens, Alejandro and Brown, Peter and Araújo, Mateus
"Semidefinite programming relaxations for quantum correlations", (2023).
- [](https://arxiv.org/abs/2311.17047) Johnston, Nathaniel and Russo, Vincent and Sikora, Jamie
"Tight bounds for antidistinguishability and circulant sets of pure quantum states", (2023).
- [](https://arxiv.org/abs/2308.15579) Pelofske, Elijah and Bartschi, Andreas and Eidenbenz, Stephan and Garcia, Bryan and Kiefer, Boris
"Probing Quantum Telecloning on Superconducting Quantum Processors", (2023).
- [](https://arxiv.org/abs/2303.07911) Philip, Aby and Rethinasamy, Soorya and Russo, Vincent and Wilde, Mark.
"Quantum Steering Algorithm for Estimating Fidelity of Separability.", Quantum 8, 1366, (2023).
- [](https://arxiv.org/abs/2302.09401) Miszczak, Jarosław Adam.
"Symbolic quantum programming for supporting applications of quantum computing technologies.", (2023).
- [](https://arxiv.org/abs/2306.09444) Casalé, Balthazar and Di Molfetta, Giuseppe and Anthoine, Sandrine and Kadri, Hachem.
"Large-Scale Quantum Separability Through a Reproducible Machine Learning Lens.", (2023).
- [](https://arxiv.org/abs/2206.08313) Russo, Vincent and Sikora, Jamie "Inner products of pure states and their antidistinguishability", Physical Review A, Vol. 107, No. 3, (2023).
## Contributing
All contributions, bug reports, bug fixes, documentation improvements,
enhancements, and ideas are welcome.
A detailed overview of how to contribute can be found in the
[contributing guide](https://toqito.readthedocs.io/en/latest/getting_started.html#contributing).
## License
[MIT License](http://opensource.org/licenses/mit-license.php>)
