Ancilla-induced amplification of quantum Fisher information

Abstract

Given a quantum state with an unknown parameter being measured with a suitable observable, Quantum Fisher Information (QFI) is the amount of information that one can extract about the unknown parameter. QFI also quantifies the maximum achievable precision in estimating the unknown parameter with a given amount of resource via 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. Using an NMR system as an example, we show that a single quadrature NMR signal of only ancillary qubits suffices to perform the quantum state tomography (QST) of target qubit's deviation part of the density matrix. We experimentally demonstrate this protocol using a star-topology spin-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 experimental QST, and estimate the amplification of QFI in each case. We also show that, in a high-temperature scenario like in the case of NMR, the QFI amplification scales linearly with the number of ancillary qubits and quadratically with the Bloch radius.