Quantifying Bell non-locality with the trace distance. (arXiv:1709.04260v1 [quant-ph])

Measurements performed on distant parts of an entangled quantum state can
generate correlations incompatible with classical theories respecting the
assumption of local causality. This is the phenomenon known as quantum
non-locality that, apart from its fundamental role, can also be put to
practical use in applications such as cryptography and distributed computing.
Clearly, developing ways of quantifying non-locality is an important primitive
in this scenario. Here, we propose to quantify the non-locality of a given
probability distribution via its trace distance to the set of classical
correlations. We show that this measure is a monotone under the free operations
of a resource theory and that furthermore can be computed efficiently with a
linear program. We put our framework to use in a variety of relevant Bell
scenarios also comparing the trace distance to other standard measures in the
literature.

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