Strengthened Bell Inequalities for Entanglement Verification

Abstract

Bell inequalities were meant to test quantum mechanics vs local hidden variable models, but can also be used to verify entanglement. For entanglement verification purposes one assumes the validity of quantum mechanics as well as quantum descriptions of one's measurements. With the help of these assumptions it is possible to derive a strengthened Bell inequality whose violation implies entanglement. We generalize known examples of such inequalities by relating the expectation value of the Bell operator to a particular quantitative measure of entanglement, namely the negativity. Moreover, we obtain statistics illustrating the fact that violating a given (strengthened or not) Bell inequality is a much more rare feat for a quantum state of two qubits than it is to be entangled.

This submission, together with the previous one, supersedes arXiv:0806.4165

References in corpus (3)

• On experimental procedures for entanglement verification
• Strengthened Bell inequalities for orthogonal spin directions
• Multi-Partite Entanglement Inequalities via Spin Vector Geometry

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• Calibration robust entanglement detection beyond Bell inequalities
• Characterizing Entanglement Sources
• Loop State-preparation-and-measurement tomography of a two-qubit system
• Detecting false correlations: Uncovering a faked Bell-inequality violation
• Entanglement Detection Beyond Local Bound with Coarse Calibrated measurements