To run the codes involving solving semi-definite programs, one has to use YALMIP as the modelling language and any solver compatible with YALMIP (e.g., SDPA, SDPT3, SDPNAL, etc.).

This project is devided into two parts:

This part contains the related MATLAB codes of the AMM, which was proposed by Chen et al. [Phys. Rev. Lett. 116, 240401 (2018)] (see https://arxiv.org/abs/1603.08532 for the arXiv preprint).

First, download all the codes and add all the files to the working path.

Files with filenames started with "ex_..." are examples.

For instance, "ex_AMM_corr_Tsirelson_bound_CHSH.m" computes an upper bound on the Tsirelson bound for a given CHSH inequality violation, using the AMM approach. In the filename, "corr" indicates that the AMM are in the form of correlators.

The other example is "ex_AMM_proj_Tsirelson_bound_elegant_BI.m", which computes an upper bound on the Tsirelson bound for a given violation of the elegant Bell inequality. In the filename, "proj" indicates that the AMM are in the form of projectors, i.e., the form that originally proposed in the paper https://arxiv.org/abs/1603.08532 .

In the above two examples, one can easily change them into any Bell scenario by adjusting the following parameters:

nx - the number of Alice's measurement settings

ny - the number of Bob's measurement settings

na - the number of Alice's measurement outcomes

nb - the number of Bob's measurement outcomes

Bell_inequality - the Bell inequality under consideration

This part includes the related MATLAB codes that computes a lower bound on the fidelity between the underlying assemblage and the reference one for a given Bell inequality violation. Ref: https://arxiv.org/abs/2002.02823

For instance, "ex_RSTA_fidelity_bound_CHSH.m" computes a lower bound on the fidelity between the underlying assemblage and the CHSH-type assemblage for a given CHSH inequality violation.