  We identify precision limits for the simultaneous estimation of multiple
parameters in multimode interferometers. Quantum strategies to enhance the
multiparameter sensitivity are based on entanglement among particles, modes or
combining both. The maximum attainable sensitivity of particle-separable states
defines the multiparameter shot-noise limit, which can be surpassed without
mode entanglement. Further enhancements up to the multiparameter Heisenberg
limit are possible by adding mode entanglement. Optimal strategies which
saturate the precision bounds are provided.

Quantum Physics