Experimental quantum-enhanced estimation of a lossy phase shift



A paradigm for quantum-enhanced precision metrology is found in optical interferometry1, which is capable of sensing diverse physical quantities through measurement of a phase shift. When standard light sources are used, the precision of the phase determination is limited by shot noise, the origin of which can be traced to the random manner in which individual photons emerge from the interferometer. Quantum entanglement provides a means to exceed this limit2,3,4,5,6 with the celebrated example of N00N states7,8,9,10, which saturate the ultimate Heisenberg limit on precision11, but are extremely fragile to losses12,13,14. In contrast, we present experimental evidence that appropriately engineered quantum states15 outperform both standard and N00N states in the precision of phase estimation when losses are present. This shows that the quantum enhancement of metrology is possible even when decoherence is present, and that the strategy for realizing the enhancement is quite distinct from protecting quantum information encoded in light16,17.

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Figure 1: Measurement of a phase shift.
Figure 2: Optimal two-photon states for phase estimation.
Figure 3: Phase dependence of two-fold coincidence rates.
Figure 4: Distributions of phase estimates.
Figure 5: Uncertainty of phase estimates.


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The authors acknowledge insightful discussions with C.M. Caves, P.G. Kwiat and K.J. Resch. This work was supported by the EU 6th Framework Programme Integrated Project Qubit Applications (contract no. 015848), the Polish Ministry of Science and Higher Education (grant no. N N202 1489 33), the Engineering and Physical Sciences Research Council (EPSRC) (grant no. EP/C546237/1) and the Royal Society.

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M.K. and W.W. assembled the experimental set-up and took measurements. R.D. conceived the experimental scheme and performed data analysis. K.B. and I.A.W. initiated and supervised the project.

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Correspondence to R. Demkowicz-Dobrzański.

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Kacprowicz, M., Demkowicz-Dobrzański, R., Wasilewski, W. et al. Experimental quantum-enhanced estimation of a lossy phase shift. Nature Photon 4, 357–360 (2010). https://doi.org/10.1038/nphoton.2010.39

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