Optimal Frames for Polarization State Reconstruction
Open accessAbstract
Complete determination of the polarization state of light requires at least four distinct projective measurements of the associated Stokes vector. Stability of state reconstruction, however, hinges on the condition number κ of the corresponding instrument matrix. Optimization of redundant measurement frames with an arbitrary number of analysis states, m, is considered in this Letter in the sense of minimization of κ. The minimum achievable κ is analytically found and shown to be independent of m, except for m=5 where this minimum is unachievable. Distribution of the optimal analysis states over the Poincaré sphere is found to be described by spherical 2 designs, including the Platonic solids as special cases. Higher order polarization properties also play a key role in nonlinear, stochastic, and quantum processes. Optimal measurement schemes for nonlinear measurands of degree t are hence also considered and found to correspond to spherical 2t designs, thereby constituting a generalization of the concept of mutually unbiased bases.
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The equal spacing of vectors around the Bloch sphere gives the device maximum robustness to errors in the tomography procedure, by essentially realizing non-local measurements.
“The equal spacing of vectors around the Bloch sphere gives the device maximum robustness to errors in the tomography procedure, 29 by essentially realizing non-local measurements.”
From Scalable on-chip quantum state tomography (2018) · cites this paper as [29]
The paper links optimal measurement frames on the Poincaré sphere to reduced error amplification in polarization reconstruction (pp. 1–3). It describes the Bloch sphere only as a geometric parallel that may inform two-level quantum tomography (p. 4); it does not say that the device achieves robustness by realizing non-local measurements. (LLM, conf=0.86)
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Gil, J. J. (2007) · The European Physical Journal Applied Physics · doi:10.1051/epjap:2007153 · Cited by 272 · see citing works
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Research works printed but not linked: 5
- [5]J. N. Damask, Polarization Optics in Telecommunications , Springer Series in Optical Sciences (SpringerVerlag, New York, New York, 2005).
- [11]A. S. Alenin, Matrix Structure for Information Driven Polarimeter Design PhD Thesis (University of Arizona, 2015).
- [29]V. V. Prasolov, Problems and theorems in linear algebra , vol. 134 of Translations of Mathematical Monographs (American Mathematical Society, Providence, RI, 1994).
- [32]A. Klappenecker and M. R¨ otteler, 'Mutually unbiased bases are complex projective 2-designs,' arXiv:quantph/0502031 (2005).
- [37]D. Cox, J. Little, and D. O'Shea, Ideals, varieties, and algorithms (Springer-Verlag, Berlin, 2007).
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Scalable on-chip quantum state tomography
Titchener, J. G., Gräfe, M., Heilmann, R., Solntsev, A. S., Szameit, A., & Sukhorukov, A. A. (2018) · npj Quantum Information · doi:10.1038/s41534-018-0063-5 · Cited by 61 · see citing works
“The equal spacing of vectors around the Bloch sphere gives the device maximum robustness to errors in the tomography procedure, 29 by essentially realizing non-local measurements.”
Background
- Authors
- Foreman, M. R., Favaro, A., & Aiello, A.
- Affiliations
- Max Planck Institute for the Science of Light (DE)
- Imperial College London (GB)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2015-12-23
- Volume
- 115
- Issue
- 26
- Pages
- 263901-263901
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2214724883
- Cited by
- 90
- References
- 1
- Citations by year
- 2026: 3 · 2025: 9 · 2024: 9 · 2023: 7 · 2022: 9 · 2021: 5 · 2020: 8 · 2019: 16 · 2018: 9 · 2017: 6 · 2016: 9
- FWCI
- 3.98
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- Spiral (Imperial College London) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Gordon and Betty Moore Foundation
- Max-Planck-Gesellschaft
- Topics
- Physical Sciences › Engineering › Biomedical Engineering › Optical Polarization and Ellipsometry
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Orbital Angular Momentum in Optics
- Keywords
- Stokes vector, condition number minimization, Poincaré sphere, Platonic solids, mutually unbiased bases, quantum state tomography
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