Ancilla Induced Amplification of Quantum Fisher Information

Abstract: Given a quantum state with an unknown parameter, the Quantum Fisher Information (QFI) is a measure of the amount of information that an observable can extract about the parameter. QFI also quantifies the maximum achievable precision in estimating the parameter with a given amount of resource via an inequality known as quantum Cramer-Rao bound. In this work, we describe a protocol to amplify QFI of a single target qubit precorrelated with a set of ancillary qubits. A single quadrature measurement of only ancillary qubits suffices to perform the complete quantum state tomography (QST) of the target qubit. We experimentally demonstrate this protocol using an NMR system consisting of a $^{13}$C nuclear spin as the target qubit and three $^1$H nuclear spins as ancillary qubits. We prepare the target qubit in various initial states, perform QST, and estimate the amplification of QFI in each case. We also show that the QFI-amplification scales linearly with the number of ancillary qubits and quadratically with their purity.