Symmetric minimal quantum tomography by successive measurements
Open accessAbstract
We consider the implementation of a symmetric informationally complete probability-operator measurement (SIC POM) in the Hilbert space of a $d$-level system by a two-step measurement process: a diagonal-operator measurement with high-rank outcomes, followed by a rank-1 measurement in a basis chosen in accordance with the result of the first measurement. We find that any Heisenberg-Weyl group-covariant SIC POM can be realized by such a sequence where the second measurement is simply a measurement in the Fourier basis, independent of the result of the first measurement. Furthermore, at least for the particular cases studied, of dimensions 2, 3, 4, and 8, this scheme reveals an unexpected operational relation between mutually unbiased bases and SIC POMs; the former are used to construct the latter. As a laboratory application of the two-step measurement process, we propose feasible optical experiments that would realize SIC POMs in various dimensions.
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The experimental scheme uses a two-step process that breaks the SIC POM into two successive measurements, each with d outcomes: a measurement with full-rank outcomes, followed by a projective measurement on a basis chosen in accordance with the result of the first measurement.
“The experimental scheme exploits a new approach to SIC POMs that uses a two-step process: a measurement with full-rank outcomes, followed by a projective measurement on a basis that is chosen in accordance with the result of the first measurement.”
From Experimental proposal for symmetric minimal two-qubit state tomography (2012) · cites this paper as [13]
The proposal exploits a new theoretical approach for constructing SIC POMs.
“The proposal exploits a new theoretical approach for constructing SIC POMs [13].”
From Experimental proposal for symmetric minimal two-qubit state tomography (2012) · cites this paper as [13]
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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
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Research works printed but not linked: 2
- [15]C. Carmeli, T. Heinosaari, and A. Toigo, arXiv:1111.3509 (2011). · arXiv
- [18]I. Bengtsson, J. Phys.: Conf. Ser., 254 , 012007 (2010).
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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
Self-citation
- Authors
- Kalev, A., Shang, J., & Englert, B.-G.
- Affiliations
- Centre for Quantum Technologies (SG)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2012-05-17
- Volume
- 85
- Issue
- 5
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2000120412
- Cited by
- 15
- References
- 1
- Citations by year
- 2020: 1 · 2019: 1 · 2017: 1 · 2015: 3 · 2014: 2 · 2013: 6 · 2012: 1
- FWCI
- 3.78
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- National University of Singapore (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
- symmetric informationally complete measurements, quantum state tomography, successive measurements, Weyl-Heisenberg group, Fourier basis, mutually unbiased bases, d-level systems, optical experiments
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