Adaptive Choice Methods for a Multi-Stage Two-Qubit Entanglement Witnessing Protocol

To enable the widespread use of quantum communication protocols, it will be crucial to efficiently verify entanglement between qubits, sometimes in an unknown or slowly-varying entangled state. Our group has developed a multi-step adaptive protocol for verifying or witnessing entanglement with limited local measurements on many copies of a two-qubit state. Beginning with measurements in three bases, we first test six classes of witnesses {W} identified by Riccardi et al (Phys. Rev. A 101, 062319, 2020). If these witnesses do not detect entanglement in a particular state,the original measurement outcomes are used to choose a second set of measurements in two additional bases, allowing us to test three additional witness classes {W'}. We report tests on computationally generated random mixed states, which show that the two-step protocol detects entanglement in 72% of all entangled states. We present two approaches to choosing the second-stage measurements and thus the set of additional witnesses {W'}: a simple analytical method and a model obtained by using computationally generated mixed states to train a neural network with five hidden layers. We present details of both choice methods as well as extensions of the adaptive protocol beyond two steps.