Code to accompany: Device-independent and semi-device-independent entanglement certification in broadcast Bell scenarios

Flavien Hirsch, Emanuel-Cristian Boghiu, Pei-Sheng Lin, Marco Túlio Quintino, and Joseph Bowles

This is a repository for the codes used to calculate the numerical results presented in the article Device-independent and semi-device-independent entanglement certification in broadcast Bell scenarios.

MATLAB code requires:

• CVX - a free MATLAB toolbox for rapid prototyping of optimization problems.
• YALMIP - a free MATLAB toolbox for optimization modeling.
• QETLAB - a free MATLAB toolbox for quantum entanglement theory.
• MOSEK - a solver for linear and semidefinite programs with free academic licenses; the code can be perfectly adapted to use free and open sources alternatives such as CVXOPT.

The MATLAB code of this repository contains:

• PrepareAndRun_HeuristicSearchBroadcast.m: Script which is read to perform a Heuristic Search method to find the optimal visibility of a given quantum state in the broadcast nonlocality scenario. This script has several adjustable parameters such as, setting a target state and the relative noise, number of parties, number of input per parties, number of outputs.

• PrepareAndRun_SteeringHeuristicSearchBroadcast2Bobs.m: Script which is read to perform a Heuristic Search method to find the optimal visibility of a given quantum state in the broadcast steering scenario with 2 untrusted Bobs. This script has various adjustable parameters such as, setting a target state and the relative noise, number of input per parties, number of outputs.

• PrepareAndRun_SteeringHeuristicSearchBroadcast3Bobs.m: Script which is read to perform a Heuristic Search method to find the optimal visibility of a given quantum state in the broadcast steering scenario with 3 untrusted Bobs. This script allows the user to set a target state and a relative noise state.

• Various subroutines and useful functions which are commented in a way to allow the users to adapt it for similar problems.

• Scripts Sec3Sec4: This is a folder with various scripts reproducing results from Sections 3 and 4. promote_chained_1A2B.m and promote_elegant_1A2B.m, using the Symbolic Math Toolbox™, calculate the coefficients of a Bell inequality promoted to the broadcast scenario from Fig. 1a) through the construction given in the paper. PromotedElegant_visibility.m and PromotedChained_visibility.m optimize said inequalities over measurements and channel to find how robust they are to white noise when the noiseless quantum state is a maximally entangled two-qubit state. PromotedIneqs_visibility_4party.m finds the robustness to white noise of the inequalities promoted to the 4-partite broadcast scenario from Fig 1b). detectionefficiency_07355.m verifies the detection efficiency threshold of 0.7355. NS2activation_POVMstate_ineq16.m verifies the broadcast activation of NS genuine network nonlocality of a bipartite state with a local model for all general measurements.

• Scripts to verify the numerical results for broadcast steering and device-independent entanglement certification, found in the directories BroadcastSteering and entanglement_detection. For the entanglement detection results, the code RebuildPPTResult.m verifies the numerical claim in the paper.