Bell-type inequalities of $$l_1$$-norm of coherence

Liang Qiu, Fei Pan, Zhi Liu

We construct the tripartite Bell-type inequalities of product states for [Formula: see text]-norm of coherence, relative entropy of coherence and skew information. We give examples of three-qubit entangled states that violate these inequalities. Particularly, the tripartite Bell-type inequality for relative entropy of coherence is always violated by the W class pure or mixed states as well as the GHZ class pure or mixed states, being used as entanglement witness.

Piyu Li, Feng Liu, Yan-Qin Xu

Liang Qiu, Z. Liu, Pan, F.

We construct the tripartite Bell-type inequalities of product states for l1-norm of coherence, relative entropy of coherence and skew information. Some three-qubit entangled states violate these inequalities. Particulary, the tripartite Bell-type inequality for relative entropy of coherence is always violated by the W class pure or mixed states as well as the GHZ class pure or mixed states, being used as entanglement witness.

Boris S. Tsirelson

Juan Pablo Paz

Stefan Filipp, Karl Svozil

Bounds on the norm of quantum operators associated with classical Bell-type inequalities can be derived from their maximal eigenvalues. This quantitative method enables detailed predictions of the maximal violations of Bell-type inequalities.