Sensitivity versus selectivity in entanglement detection via collective witnesses

Abstract

In this paper, we introduce a supervised learning technique that harnesses artificial neural networks, along with the outcomes of collective entanglement measurements, to estimate the negativity of quantum states in two-qubit and qubit-qutrit systems. The resulting deep-learned collective entanglement witnesses offer the unique capability of continuous sensitivity and selectivity tuning. This instrument enables us to explore the tradeoff between sensitivity and selectivity in entanglement detection, a dimension not accessible to previously employed analytical witnesses. In particular, we demonstrate that there are experimentally cost-effective methods (in terms of the number of measurements) where sensitivity can be significantly improved at a slight expense of the selectivity of entanglement detection. This chosen approach is also favored due to its high generality and potential for superior performance compared to other types of entanglement witnesses. Our findings may pave the way for the development of more efficient and accurate entanglement detection methods in complex quantum systems, especially when considering realistic experimental imperfections.