Quantum metrology with partially accessible chaotic sensors

Most quantum metrology protocols harness highly entangled probe states and globally accessible measurements to surpass the standard quantum limit. However, it is challenging to satisfy these requirements in realistic many-body sensors. We demonstrate that both of these constraints can be overcome in quantum chaotic sensors. Crucially, we establish that even in the presence of partial measurement accessibility, chaotic dynamics enables initial unentangled states to exhibit Heisenberg scaling of the quantum Fisher information, $I_{\alpha}$ with time. In the weakly chaotic regime, we identify spin-coherent states placed at the edge of the regular islands in the mixed classical phase space as optimal initial states for enhanced sensitivity. On the other hand, in the strongly chaotic regime, $I_{\alpha}$ is insensitive to the choice of the initial state. Notably, quantum-enhanced sensitivity is achieved even when a very low fraction ($\sim 5\%$) of the qubits are accessible. These results establish quantum chaos as a robust resource for quantum-enhanced sensing under realistic accessibility constraints on accessibility.