Proposing a New Set of Optimal Entanglement Witnesses

Quantum entanglement can be utilized for quantum information applications, super dense coding, and secure communications. Understanding whether a state is entangled is imperative for both near and far term quantum computing. An entanglement witness is an observable whose expectation value becomes negative only for entangled states. Riccardi et al. define a set of 6 entanglement witnesses {W}. We develop two-qubit entanglement witnessing protocols that rely on a subset of the full measurements required for full state tomography, with adaptive choice of measurements if a first set fails to witness entanglement. For states whose entanglement is not witnessed by {W}, we define additional witnesses {W',W''} and use the results of the first set of measurements to choose which {W',W''} witnesses to test next, with the goal of witnessing entanglement as much as possible in a limited set of measurements. We present strategies, including one based on training a neural network, to make the adaptive choice of the second witness set.