Experimental Schmidt Decomposition and Entanglement Detection

We introduce an experimental procedure for the detection of quantum entanglement of an unknown quantum state with as few measurements as possible. The method requires neither a priori knowledge of the state nor a shared reference frame between the observers. The scheme starts with local measurements, possibly supplemented with suitable filtering, that can be regarded as calibration. Consecutive correlation measurements enable detection of the entanglement of the state. We utilize the fact that the calibration stage essentially establishes the Schmidt decomposition for pure states. Alternatively we develop a decision tree which reveals entanglement within few steps. These methods are illustrated and verified experimentally for various two-qubit entangled states.