Ancilla Induced Amplification of Quantum Fisher Information

TL;DR

This paper presents an experimental protocol using ancillary qubits to amplify the Quantum Fisher Information of a target qubit, enabling enhanced parameter estimation with minimal measurements, demonstrated via NMR system experiments.

Contribution

The work introduces a novel ancilla-based protocol for amplifying QFI, allowing complete quantum state tomography with a single quadrature measurement of ancillary qubits.

Findings

QFI amplification scales linearly with ancillary qubits

QFI amplification scales quadratically with ancillary qubits' purity

Experimental demonstration using NMR system confirms theoretical predictions

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.