Entanglement-free Heisenberg-limited phase estimation

B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, G. J. Pryde

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Measurement underpins all quantitative science. A key example is the measurement of optical phase, used in length metrology and many other applications. Advances in precision measurement have consistently led to important scientific discoveries. At the fundamental level, measurement precision is limited by the number N of quantum resources (such as photons) that are used. Standard measurement schemes, using each resource independently, lead to a phase uncertainty that scales as 1/√N - known as the standard quantum limit. However, it has long been conjectured that it should be possible to achieve a precision limited only by the Heisenberg uncertainty principle, dramatically improving the scaling to 1/N (ref. 3). It is commonly thought that achieving this improvement requires the use of exotic quantum entangled states, such as the NOON state. These states are extremely difficult to generate. Measurement schemes with counted photons or ions have been performed with N ≤ 6 (refs 6-15), but few have surpassed the standard quantum limit and none have shown Heisenberg-limited scaling. Here we demonstrate experimentally a Heisenberg-limited phase estimation procedure. We replace entangled input states with multiple applications of the phase shift on unentangled single-photon states. We generalize Kitaev's phase estimation algorithm using adaptive measurement theory to achieve a standard deviation scaling at the Heisenberg limit. For the largest number of resources used (N = 378), we estimate an unknown phase with a variance more than 10 dB below the standard quantum limit; achieving this variance would require more than 4,000 resources using standard interferometry. Our results represent a drastic reduction in the complexity of achieving quantum-enhanced measurement precision.

LanguageEnglish
Pages393-396
Number of pages4
JournalNature
Volume450
Issue number7168
DOIs
Publication statusPublished - 15 Nov 2007

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Photons
Uncertainty
Interferometry
Ions

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Higgins, B. L., Berry, D. W., Bartlett, S. D., Wiseman, H. M., & Pryde, G. J. (2007). Entanglement-free Heisenberg-limited phase estimation. Nature, 450(7168), 393-396. https://doi.org/10.1038/nature06257
Higgins, B. L. ; Berry, D. W. ; Bartlett, S. D. ; Wiseman, H. M. ; Pryde, G. J. / Entanglement-free Heisenberg-limited phase estimation. In: Nature. 2007 ; Vol. 450, No. 7168. pp. 393-396.
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Higgins, BL, Berry, DW, Bartlett, SD, Wiseman, HM & Pryde, GJ 2007, 'Entanglement-free Heisenberg-limited phase estimation', Nature, vol. 450, no. 7168, pp. 393-396. https://doi.org/10.1038/nature06257

Entanglement-free Heisenberg-limited phase estimation. / Higgins, B. L.; Berry, D. W.; Bartlett, S. D.; Wiseman, H. M.; Pryde, G. J.

In: Nature, Vol. 450, No. 7168, 15.11.2007, p. 393-396.

Research output: Contribution to journalArticleResearchpeer-review

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Higgins BL, Berry DW, Bartlett SD, Wiseman HM, Pryde GJ. Entanglement-free Heisenberg-limited phase estimation. Nature. 2007 Nov 15;450(7168):393-396. https://doi.org/10.1038/nature06257