Optimal quantum estimation of the coupling constant of Jaynes-Cummings interaction

TL;DR

This paper investigates the optimal estimation of the coupling constant in the Jaynes-Cummings model, demonstrating that specific measurements can saturate the quantum Fisher information bound, with results applicable to qubit-oscillator systems.

Contribution

It derives exact quantum Fisher information for the Jaynes-Cummings interaction and identifies optimal measurement strategies for parameter estimation.

Findings

QFI equals the number of excitations in the probe state

Population and Fock measurements saturate the Cramér-Rao bound

Local measurements remain optimal when qubit is in ground or excited state

Abstract

We address the estimation of the coupling constant of the Jaynes-Cummings Hamiltonian for a coupled qubit-oscillator system. We evaluate the quantum Fisher Information (QFI) for the system undergone the Jaynes-Cummings evolution, considering that the probe initial state is prepared in a Fock state for the oscillator and in a generic pure state for the qubit; we obtain that the QFI is exactly equal to the number of excitations present in the probe state. We then focus on the two subsystems, namely the qubit and the oscillator alone, deriving the two QFIs of the two reduced states, and comparing them with the previous result. Next we focus on feasible measurements on the system, and we find out that if population measurement on the qubit and Fock number measurement on the oscillator are performed together, the Cramer-Rao bound is saturated, that is the corresponding Fisher Information (FI) is always equal to the QFI. We compare also the performances of these measurements performed alone, that is when one of the two subsystem is ignored. We show that, when the qubit is prepared in either the ground or the excited state, the local measurements are still optimal.