  Squeezing currently represents the leading strategy for quantum enhanced
precision measurements of a single parameter in a variety of continuous- and
discrete-variable settings and technological applications. However, many
important physical problems including imaging and field sensing require the
simultaneous measurement of multiple unknown parameters. The development of
multiparameter quantum metrology is yet hindered by the intrinsic difficulty in
finding 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 generalize
widely-used spin- or quadrature-squeezing parameters. Multiparameter squeezing
provides a practical and versatile concept that paves the way to the
development of quantum-enhanced estimation of multiple phases, gradients, and
fields, and for the efficient characterization of multimode quantum states in
atomic and optical sensor networks.
