Quantifying Bell non-locality with the trace distance

Abstract

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.

13 pages, 9 figures

References in corpus (11)

• Device-independent security of quantum cryptography against collective attacks
• Bounding the set of quantum correlations
• The resource theory of quantum reference frames: manipulations and monotones
• The Communication Cost of Simulating Bell Correlations
• Relaxed Bell inequalities and Kochen-Specker theorems
• The contextual fraction as a measure of contextuality
• A unifying framework for relaxations of the causal assumptions in Bell's theorem
• Bound non-locality and activation
• Maximum nonlocality in the (3,2,2) scenario
• Nonlocality free wirings and the distinguishability between Bell boxes
• Bell scenarios with communication

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