Characterization of High-Dimensional Entangled Systems via Mutually Unbiased Measurements
Open accessAbstract
Mutually unbiased bases (MUBs) play a key role in many protocols in quantum science, such as quantum key distribution. However, defining MUBs for arbitrary high-dimensional systems is theoretically difficult, and measurements in such bases can be hard to implement. We show experimentally that efficient quantum state reconstruction of a high-dimensional multipartite quantum system can be performed by considering only the MUBs of the individual parts. The state spaces of the individual subsystems are always smaller than the state space of the composite system. Thus, the benefit of this method is that MUBs need to be defined for the small Hilbert spaces of the subsystems rather than for the large space of the overall system. This becomes especially relevant where the definition or measurement of MUBs for the overall system is challenging. We illustrate this approach by implementing measurements for a high-dimensional system consisting of two photons entangled in the orbital angular momentum degree of freedom, and we reconstruct the state of this system for dimensions of the individual photons from d = 2 to 5.
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South African researchers have made seminal contributions to quantum tools including quantum channel analysis, high-dimensional state engineering, and measurement of high-dimensional states.
“Seminal contributions to quantum tools include quantum channel analysis, [26][27][28] high-dimensional state engineering, 29 and measurement of high-dimensional states.[30][31][32]”
From Toward a quantum future for South Africa (2021) · cites this paper as [30]
Cites
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Mafu, M., Dudley, A., Goyal, S., Giovannini, D., McLaren, M., Padgett, M. J., Konrad, T., Petruccione, F., Lütkenhaus, N., & Forbes, A. (2013) · Physical Review A · doi:10.1103/physreva.88.032305 · Cited by 349 · see citing works
Self-citationSelf-healing of quantum entanglement after an obstruction
McLaren, M., Mhlanga, T., Padgett, M. J., Roux, F. S., & Forbes, A. (2014) · Nature Communications · doi:10.1038/ncomms4248 · Cited by 174 · see citing works
Self-citationToward a quantum future for South Africa
Forbes, A., Petruccione, F., & Roux, F. S. (2021) · AVS Quantum Science · doi:10.1116/5.0060426 · Cited by 10 · see citing works
Self-citation
- Authors
- Giovannini, D., Romero, J., Leach, J., Dudley, A., Forbes, A., & Padgett, M. J.
- Affiliations
- University of Glasgow (GB)
- University of Strathclyde (GB)
- Heriot-Watt University (GB)
- Council for Scientific and Industrial Research (ZA)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2013-04-02
- Volume
- 110
- Issue
- 14
- Pages
- 143601-143601
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2121177239
- Cited by
- 112
- References
- 4
- Citations by year
- 2026: 6 · 2025: 8 · 2024: 8 · 2023: 7 · 2022: 8 · 2021: 9 · 2020: 9 · 2019: 10 · 2018: 15 · 2017: 9 · 2016: 7 · 2015: 6 · 2014: 6 · 2013: 4
- FWCI
- 8.48
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Physical Review Letters (publishedVersion, cc-by)
- PubMed (publishedVersion)
- ENLIGHTEN (Jurnal Bimbingan dan Konseling Islam) (acceptedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Royal Society
- Engineering and Physical Sciences Research Council (EP/I012451/1)
- 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 › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Orbital Angular Momentum in Optics
- Keywords
- mutually unbiased bases, high-dimensional quantum systems, quantum state tomography, multipartite entanglement, orbital angular momentum, photon entanglement
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