From SICs and MUBs to Eddington
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This is a survey of some very old knowledge about Mutually Unbiased Bases (MUB) and Symmetric Informationally Complete POVMs (SIC). In prime dimensions the former are closely tied to an elliptic normal curve symmetric under the Heisenberg group, while the latter are believed to be orbits under the Heisenberg group in all dimensions. In dimensions 3 and 4 the SICs are understandable in terms of elliptic curves, but a general statement escapes us. The geometry of the SICs in 3 and 4 dimensions is discussed in some detail.
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The SIC POM in dimension 4 is composed of 16 subnormalized projectors onto 16 fiducial kets.
“This SIC POM is composed of 16 subnormalized projectors onto 16 (fiducial) kets.”
From Experimental proposal for symmetric minimal two-qubit state tomography (2012) · cites this paper as [16]
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Cites
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Tadej, W., & Życzkowski, K. (2006) · Open Systems & Information Dynamics · doi:10.1007/s11080-006-8220-2 · Cited by 263 · see citing works
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Experimental proposal for symmetric minimal two-qubit state tomography
Kalev, A., Shang, J., & Englert, B.-G. (2012) · Physical Review A · doi:10.1103/physreva.85.052115 · Cited by 13 · see citing works
- Authors
- Bengtsson, I.
- Affiliations
- Stockholm University (SE)
- Corresponding author
- Bengtsson, Ingemar
- ORCID
- Bengtsson, Ingemar
- Venue
- Journal of Physics: Conference Series
- Publisher
- IOP Publishing
- Published
- 2010-11-01
- Volume
- 254
- Pages
- 012007
- ISSN
- 1742-6588 (ISSN-L)
- 1742-6596
- OpenAlex
- W1987245344
- Cited by
- 37
- References
- 1
- Citations by year
- 2025: 2 · 2024: 1 · 2022: 1 · 2021: 6 · 2020: 1 · 2017: 4 · 2016: 3 · 2015: 3 · 2014: 5 · 2013: 7 · 2012: 2
- FWCI
- 2.84
- Type
- conference paper
- Language
- en
- Open access
- diamond
- doi.org
- Locations
- Journal of Physics Conference Series (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- mutually unbiased bases, symmetric informationally complete POVM, small incision cataract surgery, Eddington number, Heisenberg group, prime dimension, quantum state tomography, finite-dimensional quantum systems
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