Chain Inequality Violation with Quantum Weak Measurement Technology

Bell inequality is an important resource in the quantum information theory, which can be applied to guarantee security of the device independent quantum information protocols. By utilizing the quantum weak measurement technology, we propose the Chain inequality violation with three parties, and the analysis result demonstrates that double Chain inequality violation can be observed in the case of Alice and Bob have two different measurement bases. Since the weak measurement model can be assumed to be an eavesdropping model, our analysis model may be applied to analyze security of the device independent quantum information protocols.