Scalable Heisenberg limited metrology using mixed states

Improving the precision of measurements is a prime challenge to the scientific community. Quantum metrology provides methods to overcome the standard quantum limit (SQL) of 1/sqrt{N} and to reach the fundamental Heisenberg-limit (HL) of 1/N. While a lot of theoretical and experimenta works have been dedicated to this task, most of the attempts focused on utilizing NOON and squeezed states, which exhibit unique quantum correlations. Here we present, and experimentally implement, a new scheme for precision measurements that enables reaching the HL. Our scheme is based on a probe in a mixed state with a large uncertainty, combined with a post-selection, such that the Fisher information is maximized, and the Carmer-Rao bound is saturated. We performed a Heisenberg limited measurement of the Kerr non-linearity of a single photon, where an ultra-small Kerr phase of 6 *10^{-8}$ was observed with an unprecedented precision of 10^{-9}. Our method paves the way to Heisenberg-limited metrology with only mixed state.