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Phase-space formulation of quantum mechanics and quantum-state reconstruction for physical systems with Lie-group symmetries
Open accessAbstract
We present a detailed discussion of a general theory of phase-space distributions, introduced recently by the authors [J. Phys. A 31, L9 (1998)]. This theory provides a unified phase-space formulation of quantum mechanics for physical systems possessing Lie-group symmetries. The concept of generalized coherent states and the method of harmonic analysis are used to construct explicitly a family of phase-space functions which are postulated to satisfy the Stratonovich-Weyl correspondence with a generalized tracing condition. The symbol calculus for the phase-space functions is given by means of the generalized twisted product. The phase-space formalism is used to study the problem of the reconstruction of quantum states. In particular, we consider the reconstruction method based on measurements of displaced projectors, which comprises a number of recently proposed quantum-optical schemes and is also related to the standard methods of signal processing. A general group-theoretic description of this method is developed using the technique of harmonic expansions on the phase space.
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Cites
On the Quantum Correction For Thermodynamic Equilibrium
Wigner, E. (1932) · Physical Review · doi:10.1103/physrev.40.749 · Cited by 9,283
Quantum mechanics as a statistical theory
Moyal, J. E. (1949) · Mathematical Proceedings of the Cambridge Philosophical Society · doi:10.1017/s0305004100000487 · Cited by 3,116
Description of States in Quantum Mechanics by Density Matrix and Operator Techniques
Fano, U. (1957) · Reviews of Modern Physics · doi:10.1103/revmodphys.29.74 · Cited by 1,975
Smithey, D. T., Beck, M., Raymer, M. G., & Faridani, A. (1993) · Physical Review Letters · doi:10.1103/physrevlett.70.1244 · Cited by 1,538
Experimental Determination of the Motional Quantum State of a Trapped Atom
Leibfried, D., Meekhof, D. M., King, B. E., Monroe, C., Itano, W. M., & Wineland, D. J. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.4281 · Cited by 688
Detection of the density matrix through optical homodyne tomography without filtered back projection
D’Ariano, G. M., Macchiavello, C., & Paris, M. G. A. (1994) · Physical Review A · doi:10.1103/physreva.50.4298 · Cited by 218
Cited by
Variational-state quantum metrology
Koczor, B., Endo, S., Jones, T., Matsuzaki, Y., & Benjamin, S. C. (2020) · New Journal of Physics · doi:10.1088/1367-2630/ab965e · Cited by 101
Metadata
- Authors
- Brif, C., & Mann, A.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1999-02-01
- Volume
- 59
- Issue
- 2
- Pages
- 971-987
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2078412318
- Cited by
- 222
- References
- 6
- FWCI
- 4.94
- Type
- journal article
- Language
- en
- Open access
- green
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- Brif, C., & Mann, A. (1999). Phase-space formulation of quantum mechanics and quantum-state reconstruction for physical systems with Lie-group symmetries. Physical Review A. https://doi.org/10.1103/physreva.59.971
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