



01434nas a2200145   4500008004100000245005900041210005800100260001400158490000600172520100600178100002001184700002201204700002501226856003701251       2023                        eng d00aMinimum-entanglement protocols for function estimation0 aMinimumentanglement protocols for function estimation  c9/29/20230 v53 a<p>We derive a family of optimal protocols, in the sense of saturating the quantum Cramér-Rao bound, for measuring a linear combination of d field amplitudes with quantum sensor networks, a key subprotocol of general quantum sensor network applications. We demonstrate how to select different protocols from this family under various constraints. Focusing primarily on entanglement-based constraints, we prove the surprising result that highly entangled states are not necessary to achieve optimality in many cases. Specifically, we prove necessary and sufficient conditions for the existence of optimal protocols using at most k-partite entanglement. We prove that the protocols which satisfy these conditions use the minimum amount of entanglement possible, even when given access to arbitrary controls and ancilla. Our protocols require some amount of time-dependent control, and we show that a related class of time-independent protocols fail to achieve optimal scaling for generic functions.</p>1 aEhrenberg, Adam1 aBringewatt, Jacob1 aGorshkov, Alexey, V.  uhttps://arxiv.org/abs/2110.07613