Saturation of Quantum Cramer-Rao Bounds for Distributed Sensing via Error Sensitivity in SU(1,1)-SU(m) Interferometry

Abstract: Breaking the standard quantum limit in the sensing of parameters at different spatial locations, such as in a quantum network, is of great importance. Using the framework of quantum Fisher information, many strategies based on squeezed quantum probes and multipath multiphoton or multiqubit entangled states have been considered. In this context there is always the question of what is the simplest measurement that would saturate quantum Cramer-Rao bound (QCRB). The simplest quantity to measure would be characteristics of photon flux or population distribution in case of qubits. Previous studies have shown that the error sensitivity in SU(1,1) interferometry, also known by several other names as nonlinear interferometry, time reversed measurements; does saturate QCRB for single parameters like phase, displacement, loss. In this work we bring out great utility of generalized SU(1,1) interferometry in distributed sensing. The generalized SU(1,1) interferometry is a combination of SU(m) and SU(1,1) elements, where m is the number of nodes in the network. The SU(m) element is used to produce distributed entanglement starting from a squeezed photonic or matter probe. We demonstrate how error sensitivity measurement at just one output port can saturate or nearly saturate QCRB and thus results in Heisenberg sensitivity of network sensing.