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We simulate the dynamics of systems with $N$ = 1-20 qubits coupled to acavity in order to assess their potential for quantum metrology of a parameterin the open systems limit. The qubits and the cavity are both allowed to havelosses and the system is studied under various coupling strength regimes. Thefocus is primarily on the coupling between the qubits using the quantum Fisherinformation as the measured parameter. Some results on estimating thequbit-cavity detuning parameter are also presented. We investigate the scalingof the uncertainty in the estimate of the qubit-cavity coupling with the numberof qubits and for different initial states of the qubits that act as thequantum probe. As initial probe states, we consider Dicke states with varyingexcitation numbers, the GHZ state, and separable X-polarized states. It isshown that in the strong coupling regime, i.e., when the coupling between thequbits and the cavity is greater than the decay parameters of both the qubitsand the cavity, Dicke states with a large excitation number can achieve theHeisenberg limit, with the precision scaling improving as the excitation numberincreases. A particularly intriguing finding of our study is that in the weakcoupling regime, as well as in situations where either the qubit or cavitydecay parameters exceed the coupling, the separable $X$-polarized state is thebest in terms of scaling and is even able to achieve the Heisenberg limit inthese lossy regimes for the range of $N$ considered.

Enhanced quantum sensing mediated by a cavity in open systems