A Geometric Approach To Adaptive Entanglement Witnessing

Detecting or witnessing quantum entanglement is imperative for near and long-term applications in secure quantum communication. We present an adaptive protocol to detect entanglement with local measurements on multiple copies of an unknown two-qubit state. After an initial set of measurements, if entanglement is not witnessed, the original measurement outcomes are used to select the next stage of measurements most likely to witness entanglement if it is present. Our group previously developed a two-step adaptive protocol that can detect 79% of computationally generated mixed entangled states with only 56% of the measurements required for full state tomography. We expand this protocol by introducing new sets of entanglement witnesses that include additional measurements to adaptively choose from. To construct these witnesses, we take a geometric approach of rotating the bases of either or both qubits from our previous sets of witnesses. This geometric approach allows us to construct complete sets of extremal entanglement witnesses from previous sets of witnesses. We present the logical structure and efficacy of our expanded protocol.