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Optimal Quantum Phase Estimation
Open accessAbstract
By using a systematic optimization approach, we determine quantum states of light with definite photon number leading to the best possible precision in optical two-mode interferometry. Our treatment takes into account the experimentally relevant situation of photon losses. Our results thus reveal the benchmark for precision in optical interferometry. Although this boundary is generally worse than the Heisenberg limit, we show that the obtained precision beats the standard quantum limit, thus leading to a significant improvement compared to classical interferometers. We furthermore discuss alternative states and strategies to the optimized states which are easier to generate at the cost of only slightly lower precision.
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“Moreover, as N grows, N-photon entangled states become increasingly sensitive to losses, as the loss of a single photon is enough to destroy all the phase information11.”
From Photonic polarization gears for ultra-sensitive angular measurements (2013) · cites this paper as [11]
Experimental — accuracy not yet measuredIn the citing paper
“In the presence of decoherence, the optimal input states do not have an intuitive form and the maximization of the QFI (with rising N) becomes hard even numerically202930.”
From The elusive Heisenberg limit in quantum-enhanced metrology (2012) · cites this paper as [29]
In the citing paper
“Second, as state (3) does not bear any multi-photon coherences, losses reduce the total number of photons, but leave the remaining ones unaltered. That is, total losses characterized by an overall transmissivity 0≤ η ≤1 enter as a constant multiplicative factor, simply rescaling in equation (6) the total number of photons to νNη (see Supplementary Note 1), in striking contrast to NOON states11.”
From Photonic polarization gears for ultra-sensitive angular measurements (2013) · cites this paper as [11]
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Metadata
- Authors
- Dorner, U., Demkowicz-Dobrzanski, R., Smith, B. J., Lundeen, J. S., Wasilewski, W., Banaszek, K., & Walmsley, I. A.
- Affiliations
- University of Oxford (GB)
- University of Warsaw (PL)
- Nicolaus Copernicus University (PL)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2009-01-30
- Volume
- 102
- Issue
- 4
- Pages
- 040403-040403
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2008439590
- Cited by
- 494
- References
- 19
- Citations by year
- 2026: 23 · 2025: 39 · 2024: 27 · 2023: 26 · 2022: 27 · 2021: 19 · 2020: 36 · 2019: 32 · 2018: 27 · 2017: 36 · 2016: 34 · 2015: 23 · 2014: 39 · 2013: 28 · 2012: 23
- FWCI
- 28.07
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Engineering and Physical Sciences Research Council (GR/S82176/01, EP/E036066/1)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum optics and atomic interactions
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- quantum phase estimation, photon number states, photon loss, standard quantum limit, Heisenberg limit, quantum metrology, squeezed light
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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