Experimental characterization of qutrits using symmetric informationally complete positive operator-valued measurements
Open accessAbstract
Generalized quantum measurements [also known as positive operator-valued measures (POVMs)] are of great importance in quantum information and quantum foundations but are often difficult to perform. We present an experimental approach which can in principle be used to perform arbitrary POVMs in a linear-optical context. One of the most interesting POVMs, the symmetric informationally complete (SIC) POVM, is the most compact set of measurements that can be used to fully describe a quantum state. We use our technique to carry out the first experimental characterization of the state of a qutrit using SIC POVMs. Because of the highly symmetric nature of this measurement, such a representation has the unique property that it permits all other measurement outcomes to be predicted by a simple extension of the classical Bayesian sum rule, making no use of complex amplitudes or Hilbert-space operators. We demonstrate this approach on several qutrit states encoded in single photons.
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All experiments and proposals for experiments implementing SIC POMs up to date have been limited to the two-level system (qubit), with the exception of one where a SIC POM for a three-level system was approximated.
“In contrast to the major theoretical progress, up to date, all experiments and even proposals for experiments implementing SIC POMs have been limited to the very basic quantum system, the two-level system (qubit) [10, 11], with the exception of [12] where a SIC POM for a three-level system was approximated.”
From Experimental proposal for symmetric minimal two-qubit state tomography (2012) · cites this paper as [12]
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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
- Medendorp, Z. E. D., Torres-Ruiz, F. A., Shalm, L. K., Tabia, G. N. M., Fuchs, C. A., & Steinberg, A. M.
- Affiliations
- University of Toronto (CA)
- Universidad de La Frontera (CL)
- Perimeter Institute (CA)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2011-05-11
- Volume
- 83
- Issue
- 5
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1561042475
- Cited by
- 89
- References
- 0
- Citations by year
- 2026: 2 · 2025: 3 · 2024: 3 · 2023: 5 · 2022: 7 · 2021: 7 · 2020: 9 · 2019: 6 · 2018: 5 · 2017: 5 · 2016: 2 · 2015: 6 · 2014: 7 · 2013: 8 · 2012: 9
- FWCI
- 8.54
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Omeka S (Universidad de La Frontera) (submittedVersion, cc-by-nc-nd)
- 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
- qutrits, symmetric informationally complete POVM, SIC-POVM, generalized quantum measurements, linear optics, quantum state tomography, quantum foundations
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