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Implementation of a canonical phase measurement with quantum feedback


Much of modern metrology and communication technology encodes information in electromagnetic waves, typically as an amplitude or phase. Although current hardware can perform near-ideal measurements of photon number or field amplitude, the ability to perform an ideal phase measurement is still lacking, even in principle. In this work, we implement a single-shot canonical phase measurement on a one-photon wave packet, which surpasses the current standard of heterodyne detection and is optimal for single-shot phase estimation. By applying quantum feedback to a Josephson parametric amplifier, our system adaptively changes its measurement basis during photon arrival and allows us to validate the detector’s performance by tracking the quantum state of the photon source. These results demonstrate that quantum feedback can both enhance the precision of a detector and enable it to measure new classes of physical observables.

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Fig. 1: Experimental implementation.
Fig. 2: Measurement back-action and quantum trajectories.
Fig. 3: Back-action and measurement validation.
Fig. 4: Phase-estimation performance.

Data availability

Source data are available for this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding author on reasonable request.


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We thank E. Flurin, J.M. Kreikebaum and V.V. Ramasesh for assistance, and MIT Lincoln labs for fabrication of the travelling wave parametric amplifier. This work was supported by the Army Research Office under Grant Number W911NF15-1-0496. L.S.M. was supported by National Science Foundation Grant Number 1106400 and the Berkeley Fellowship for Graduate Study.

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Authors and Affiliations



L.S.M. and H.M.W. conceived of the experiment with assistance from S.H.-G. L.S.M., S.H.-G. and W.P.L. constructed the experiment. S.H.-G. fabricated the qubit and Josephson parametric amplifier, and W.P.L. programmed the FPGA. L.S.M. and W.P.L. conducted the experiment. L.S.M. analysed the data and wrote the manuscript with assistance from W.P.L. All work was carried out under the supervision of H.M.W. and I.S.

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Correspondence to Leigh S. Martin.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Naoki Yamamoto and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary information and Figs. 1–6.

Source data

Source Data Fig. 1

x and y axes of Fig. 1c.

Source Data Fig. 3

x and y axes of Fig. 3b, histogram data of Fig. 3d.

Source Data Fig. 4

Histogram data (x and y axes) for Fig. 4a and Fig. 4c.

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Martin, L.S., Livingston, W.P., Hacohen-Gourgy, S. et al. Implementation of a canonical phase measurement with quantum feedback. Nat. Phys. 16, 1046–1049 (2020).

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