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Heisenberg uncertainty relation in quantum mechanics sets the limit on themeasurement precision of non-commuting observables, which prevents us frommeasuring them accurately at the same time. In some applications, however, theinformation are embedded in two or more non-commuting observables. On the otherhand, quantum entanglement allows us to infer through Einstein-Podolsky-Rosencorrelations two conjugate observables with precision better than what isallowed by Heisenberg uncertainty relation. With the help of the newlydeveloped SU(1,1) interferometer, we implement a scheme to measure jointlyinformation encoded in multiple non-commuting observables of an optical fieldwith a signal-to-noise ratio improvement of about 20 % over the standardquantum limit on all measured quantities simultaneously. This scheme can begeneralized to the joint measurement of information in arbitrary number ofnon-commuting observables.

Quantum enhanced joint measurement of multiple non-commuting observables with SU(1,1) interferometer