Entanglement-enhanced multiparameter sensing: leveraging cavity-mediated programmable interactions

Entanglement is a powerful resource for improving the precision of quantum measurements. All-to-all entanglement that is naturally generated by long-range interactions in optical cavities is optimally suited to single parameter estimation tasks, such as timekeeping or sensing global fields. In our system, we combine global cavity-mediated interactions with local rotations to create multimode entangled states that are useful for a wider variety of quantum sensing tasks. As a specific example, we produce a two-mode squeezed state (EPR state). By treating one subsystem as a sensing region and the other as an ancilla or quantum memory, we achieve simultaneous sensitivity to displacements of two conjugate quadratures in the sensing region. Using an echo-based protocol, we simultaneously read out both quadratures with a sensitivity surpassing the local Heisenberg limit. This simultaneous sensitivity to conjugate displacements promises a provable speedup for sensing tasks such as characterizing bosonic random displacement channel. Our general method is scalable to larger and more complex graphs, laying groundwork for advanced quantum metrology protocols such as quantum compressed sensing.