Bell-type inequality in quantum coherence theory as an entanglement witness

Understand

Bell inequality is a mathematical inequality derived using the assumptions of locality and realism.

• Its violation guarantees the existence of quantum correlations in a quantum state.
• Bell inequality acts as an entanglement witness in the sense that a pure bipartite quantum state, having nonvanishing entanglement, always violates a Bell inequality.
• We construct Bell-type inequalities for product states in quantum coherence theory for different measures of coherence, and find that the maximally entangled states violate these inequalities.