The DOI matches its Crossref record; 21 of the 21 references it cites were found in a registry or an index.
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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Citations
Cites
Quantum detection and estimation theory
Helstrom, C. W. (1969) · Journal of Statistical Physics · doi:10.1007/bf01007479 · Cited by 3,776
Statistical distance and the geometry of quantum states
Braunstein, S. L., & Caves, C. M. (1994) · Physical Review Letters · doi:10.1103/physrevlett.72.3439 · Cited by 3,176
Quantum-Enhanced Measurements: Beating the Standard Quantum Limit
Giovannetti, V., Lloyd, S., & Maccone, L. (2004) · Science · doi:10.1126/science.1104149 · Cited by 3,160
Probabilistic and Statistical Aspects of Quantum Theory
Holevo, A. (2011) · doi:10.1007/978-88-7642-378-9 · Cited by 2,582
Giovannetti, V., Lloyd, S., & Maccone, L. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.010401 · Cited by 2,440
Optimal frequency measurements with maximally correlated states
Bollinger, J. J., Itano, W. M., Wineland, D. J., & Heinzen, D. J. (1996) · Physical Review A · doi:10.1103/physreva.54.r4649 · Cited by 1,167
Improvement of Frequency Standards with Quantum Entanglement
Huelga, S. F., Macchiavello, C., Pellizzari, T., Ekert, A. K., Plenio, M. B., & Cirac, J. I. (1997) · Physical Review Letters · doi:10.1103/physrevlett.79.3865 · Cited by 999
Interferometric detection of optical phase shifts at the Heisenberg limit
Holland, M., & Burnett, K. R. (1993) · Physical Review Letters · doi:10.1103/physrevlett.71.1355 · Cited by 864
Super-resolving phase measurements with a multiphoton entangled state
Mitchell, M. W., Lundeen, J. S., & Steinberg, A. M. (2004) · Nature · doi:10.1038/nature02493 · Cited by 830
Self-citationBeating the Standard Quantum Limit with Four-Entangled Photons
Nagata, T., Okamoto, R., O'Brien, J. L., Sasaki, K., & Takeuchi, S. (2007) · Science · doi:10.1126/science.1138007 · Cited by 735
Cited by
Sorted by citations
Giovannetti, V., Lloyd, S., & Maccone, L. (2011) · Nature Photonics · doi:10.1038/nphoton.2011.35 · Cited by 3,894
General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
Escher, B. M., de Matos Filho, R. L., & Davidovich, L. (2011) · Nature Physics · doi:10.1038/nphys1958 · Cited by 928
Advances in photonic quantum sensing
Pirandola, S., Bardhan, B. R., Gehring, T., Weedbrook, C., & Lloyd, S. (2018) · Nature Photonics · doi:10.1038/s41566-018-0301-6 · Cited by 829
The elusive Heisenberg limit in quantum-enhanced metrology
Demkowicz-Dobrzański, R., Kołodyński, J., & Guţă, M. (2012) · Nature Communications · doi:10.1038/ncomms2067 · Cited by 773
Squeezed states of light and their applications in laser interferometers
Schnabel, R. (2017) · Physics Reports · doi:10.1016/j.physrep.2017.04.001 · Cited by 562
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
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