Iterations of nonlinear entanglement witnesses

Abstract

We describe a generic way to improve a given linear entanglement witness by a quadratic, nonlinear term. This method can be iterated, leading to a whole sequence of nonlinear witnesses, which become stronger in each step of the iteration. We show how to optimize this iteration with respect to a given state, and prove that in the limit of the iteration the nonlinear witness detects all states that can be detected by the positive map corresponding to the original linear witness.

11 pages, 5 figures

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• Accessible nonlinear entanglement witnesses
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• Detecting three-qubit bound MUB diagonal entangled states via Nonlinear optimal entanglement witnesses
• Separability in terms of a single entanglement witness
• Efficient nonlinear witnessing of non-absolutely separable states with lossy detectors
• Beating detection loophole in nonlinear entanglement witnesses
• Nonlinear Improvement of Qubit-qudit Entanglement Witnesses
• Unified approach to geometric and positive-map-based non-linear entanglement identifiers
• Measurement-device-independent nonlinear entanglement witnesses
• Confident entanglement detection via separable numerical range
• Closing loopholes of measurement-device-independent nonlinear entanglement witnesses