We consider discriminating between bipartite boxes with 2 binary inputs and 2binary outputs (2x2) using the class of completely locality preservingoperations i.e. those, which transform boxes with local hidden variable model(LHVM) into boxes with LHVM, and have this property even when tensored withidentity operation. Following approach developed in entanglement theory wederive linear program which gives an upper bound on the probability of successof discrimination between different isotropic boxes. In particular we providean upper bound on the probability of success of discrimination betweenisotropic boxes with the same mixing parameter. As a counterpart ofentanglement monotone we use the non-locality cost. Discrimination isrestricted by the fact that non-locality cost does not increase underconsidered class of operations. We also show that with help of allowed class ofoperations one can distinguish perfectly any two extremal boxes in 2x2 case andany local extremal box from any other extremal box in case of two inputs andtwo outputs of arbitrary cardinalities.
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