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For the last 20 years, the question of what are the fundamental capabilitiesof quantum precision measurements has sparked a lively debate throughout thescientific community. Typically, the ultimate limits in quantum metrology areassociated with the notion of the Heisenberg limit expressed in terms of thephysical resources used in the measurement procedure. Over the years, a varietyof different physical resources were introduced, leading to a confusion aboutthe meaning of the Heisenberg limit. Here, we review the mainstream definitionsof the relevant resources and introduce the universal resource count, that is,the expectation value of the generator (above its ground state) of translationsin the parameter we wish to estimate, that applies to all measurementstrategies. This leads to the ultimate formulation of the Heisenberg limit forquantum metrology. We prove that the new limit holds for the generators oftranslations with an upper-bounded spectrum.

Ultimate limits to quantum metrology and the meaning of the Heisenberg limit