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Squeezing currently represents the leading strategy for quantum enhancedprecision measurements of a single parameter in a variety of continuous- anddiscrete-variable settings and technological applications. However, manyimportant physical problems including imaging and field sensing require thesimultaneous measurement of multiple unknown parameters. The development ofmultiparameter quantum metrology is yet hindered by the intrinsic difficulty infinding saturable sensitivity bounds and feasible estimation strategies. Here,we derive the general operational concept of multiparameter squeezing,identifying metrologically useful states and optimal estimation strategies.When applied to spin- or continuous-variable systems, our results generalizewidely-used spin- or quadrature-squeezing parameters. Multiparameter squeezingprovides a practical and versatile concept that paves the way to thedevelopment of quantum-enhanced estimation of multiple phases, gradients, andfields, and for the efficient characterization of multimode quantum states inatomic and optical sensor networks.

Multiparameter squeezing for optimal quantum enhancements in sensor networks