Tomographic Universality of the Discrete Wigner Function
Abstract
:1. Introduction
2. The Generalized Pauli Group and Displacement Operators
3. Phase Space Construction and the Wigner Map
4. Tomographic Universality of the Discrete Wigner Function
4.1. Tomographic Property for a Given DPS Partition
4.2. Odd Local Dimensions
4.3. Even Local Dimensions
- 1.
- If , then ;
- 2.
- If , then ;
- 3.
- If , there are no values producing Abelian curves, as can be observed in the example in Figure 1b, where the only Abelian curve is the ray .
- 1.
- If , then ;
- 2.
- If , then ;
- 3.
- If , .
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
Appendix B
- (a)
- Regular curves
- (b)
- Exceptional curves
Appendix C
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Sainz, I.; Camacho, E.; García, A.; Klimov, A.B. Tomographic Universality of the Discrete Wigner Function. Quantum Rep. 2024, 6, 58-73. https://doi.org/10.3390/quantum6010005
Sainz I, Camacho E, García A, Klimov AB. Tomographic Universality of the Discrete Wigner Function. Quantum Reports. 2024; 6(1):58-73. https://doi.org/10.3390/quantum6010005
Chicago/Turabian StyleSainz, Isabel, Ernesto Camacho, Andrés García, and Andrei B. Klimov. 2024. "Tomographic Universality of the Discrete Wigner Function" Quantum Reports 6, no. 1: 58-73. https://doi.org/10.3390/quantum6010005