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Description
We present a program speeding up the brute force calculation of the $L_d$ norms of an n×m matrix M. The $L_1$ norm stands for the local bound of the Bell expression [1], meanwhile, $L_d$ norms where $d \ge 2$ are the classical $d$-dimensional bounds of the prepare-and-measure (PM) witness [2]. In both cases, we assume binary outputs. These norms are of interest in the field of communication complexity, the Grothendieck constant, or in graph theory. The effectiveness of our implementation is based on two factors. On the one hand, our code capitalizes on the efficient implementation of the algorithm calculating the Ld norms using special mathematical and programming techniques. On the other hand, our code is implemented in the C programming language with OpenMP, MPI, or CUDA exploiting the advantages of shared or distributed parallelism, or capable of utilizing massively parallel platforms, namely Graphics Processing Units (GPUs).
[1] P. Diviánszky, E. Bene and T. Vértesi, Phys. Rev. A, 96 (2017) 012113
[2] P. Diviánszky, I. Márton, E. Bene and T. Vértesi, Scientific Reports, 13 (2023) 13200