Montina, Alberto Wolf, Stefan 2019-01-23 In view of the importance of quantum non-locality in cryptography, quantum computation, and communication complexity, it is crucial to decide whether a given correlation exhibits non-locality or not. As proved by Pitowski, this problem is NP- complete, and is thus computationally intractable unless NP is equal to P. In this paper, we first prove that the Euclidean distance of given correlations from the local polytope can be computed in polynomial time with arbitrary fixed error, granted the access to a certain oracle; namely, given a fixed error, we derive two upper bounds on the running time. The first bound is linear in the number of measurements. The second bound scales with the number of measurements to the sixth power. The former holds only for a very high number of measurements, and is never observed in the performed numerical tests. We, then, introduce a simple algorithm for simulating the oracle. In all of the considered numerical tests, the simulation of the oracle contributes with a multiplicative factor to the overall running time and, thus, does not affect the sixth- power law of the oracle-assisted algorithm. application/pdf https://localhost:5000/ark:/12658/srd1318939 https://susi.usi.ch/global/documents/318939 https://susi.usi.ch/documents/318939/files/Montina_E_2019.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.3390/e21020104 info:eu-repo/semantics/altIdentifier/ark/12658/srd1318939 info:eu-repo/semantics/openAccess CC BY Entropy. - 2019, vol. 21, no. 2, p. 104 Local polytope Quantum nonlocality Communication complexity Optimization info:eu-repo/classification/udc/004 Discrimination of non-local correlations http://purl.org/coar/resource_type/c_6501