Code to accompany: Semi-device-independent certification of indefinite causal order

Jessica Bavaresco, Mateus Araújo, Časlav Brukner, and Marco Túlio Quintino

This is a repository for the code used to calculate the numerical results summarized in Table II of the article "Semi-device-independent certification of indefinite causal order, Jessica Bavaresco, Mateus Araújo, Časlav Brukner, Marco Túlio Quintino, Quantum 3, 176 (2019), arXiv:1903.10526 [quant-ph]".

All code is written in MATLAB and requires:

• Yalmip - a free MATLAB toolbox for rapid prototyping of optimization problems
• MOSEK - a software package for solving mathematical optimization problems (under the free personal academic license)
• QETLAB - a free MATLAB toolbox for quantum entanglement theory

This repository consists in the following four SDPs plus a function that defines the quantum switch process and sets of instruments used in our work, and calculates the non-zero values of Table II.

• randrobust_tripartiteW_TTT: Calculates the \eta^* of a tripartite process matrix in the TTT scenario.

• randrobust_tripartiteW_TTU: Calculates a lower bound for \eta^* of a tripartite process matrix in the TTU scenario, using a given set of POVMs for Charlie.

• randrobust_tripartiteW_TUU: Calculates a lower bound for \eta^* of a tripartite process matrix in the TUU scenario, using a given set of instruments for Bob and a set of POVMs for Charlie.

• randrobust_tripartiteW_UTT: Calculates a lower bound for \eta^* of a tripartite process matrix in the UTT scenario, using a given set of instruments for Alice.

• switch_randrobustness: Defines the quantum switch process and the sets of instruments used in our work, provides them as input to the four previous SDPs and outputs the values of/bounds for \eta^*.