Detecting entanglement of unknown states by violating the Clauser-Horne-Shimony-Holt inequality

Entangled states play a fundamental role in Quantum Mechanics and are at the core of many contemporary applications, such as quantum communication and quantum computing. Therefore, determining whether a state is entangled or not is an important task. Here, we propose a method to detect the entanglement of unknown two-qubit quantum states. Our method is based on the violation of the Clauser-Horne-Shimony-Holt inequality. This maximizes the value of the inequality even when \lp{it} contains an unknown quantum state. The method iteratively generates local measurement settings that lead to increasing values of the inequality. We show by numerical simulations for pure and mixed states that our algorithm exceeds the classical limit of 2 after a few iterations.