Ultimate quantum sensitivity in the 3D relative localisation of two single-photon emitters via two-photon interference

Abstract We present a quantum sensing protocol for the simultaneous estimation of the difference in the localization parameters of two single-photon sources, paving the way to single-photon 3D imaging and 3D nanoscopy beyond the diffraction limit. This is achieved by exploiting two-photon interference of the two emitted photons at a beam splitter via sampling measurements in the frequency and transverse momenta at the output. We prove theoretically that this technique reaches the ultimate sensitivity in the 3D relative localization of two emitters, already with a number of sampling measurements of $$\sim 2000$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>2000</mml:mn> </mml:mrow> </mml:math> and a bias in the three localization parameters below $$1\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> . These results are independent of the values of the localization parameters to estimate.