Physics:Wigner–Araki–Yanase theorem
The Wigner–Araki–Yanase theorem, also known as the WAY theorem, is a result in quantum physics establishing that the presence of a conservation law limits the accuracy with which observables that fail to commute with the conserved quantity can be measured.[1][2][3] It is named for the physicists Eugene Wigner,[4] Huzihiro Araki and Mutsuo Yanase.[5][6] The theorem can be illustrated with a particle coupled to a measuring apparatus.[7]:421 If the position operator of the particle is [math]\displaystyle{ q }[/math] and its momentum operator is [math]\displaystyle{ p }[/math], and if the position and momentum of the apparatus are [math]\displaystyle{ Q }[/math] and [math]\displaystyle{ P }[/math] respectively, assuming that the total momentum [math]\displaystyle{ p + P }[/math] is conserved implies that, in a suitably quantified sense, the particle's position itself cannot be measured. The measurable quantity is its position relative to the measuring apparatus, represented by the operator [math]\displaystyle{ q - Q }[/math]. The Wigner–Araki–Yanase theorem generalizes this to the case of two arbitrary observables [math]\displaystyle{ A }[/math] and [math]\displaystyle{ B }[/math] for the system and an observable [math]\displaystyle{ C }[/math] for the apparatus, satisfying the condition that [math]\displaystyle{ B + C }[/math] is conserved.[8][9]
Mikko Tukiainen gave a generalized version of the WAY theorem, which makes no use of conservation laws, but uses quantum incompatibility instead.[10]
Yui Kuramochi and Hiroyasu Tajima proved a generalized form of the theorem for possibly unbounded and continuous conserved observables.[11]
References
- ↑ Baez, John C. (1994-05-10). "Week 33". http://math.ucr.edu/home/baez/week33.html.
- ↑ Ahmadi, Mehdi; Jennings, David; Rudolph, Terry (2013-01-28). "The Wigner–Araki–Yanase theorem and the quantum resource theory of asymmetry" (in en). New Journal of Physics 15 (1): 013057. doi:10.1088/1367-2630/15/1/013057. ISSN 1367-2630.
- ↑ Loveridge, L.; Busch, P. (2011). "'Measurement of quantum mechanical operators' revisited" (in en). The European Physical Journal D 62 (2): 297–307. doi:10.1140/epjd/e2011-10714-3. ISSN 1434-6060. Bibcode: 2011EPJD...62..297L.
- ↑ Wigner, E. P. (1995), Mehra, Jagdish, ed., "Die Messung quantenmechanischer Operatoren" (in en), Philosophical Reflections and Syntheses (Springer Berlin Heidelberg): pp. 147–154, doi:10.1007/978-3-642-78374-6_10, ISBN 978-3-540-63372-3. For an English translation, see Busch, P. (2010). "Translation of "Die Messung quantenmechanischer Operatoren" by E.P. Wigner". arXiv:1012.4372 [quant-ph].
- ↑ Araki, Huzihiro; Yanase, Mutsuo M. (1960-10-15). "Measurement of Quantum Mechanical Operators" (in en). Physical Review 120 (2): 622–626. doi:10.1103/PhysRev.120.622. ISSN 0031-899X. https://link.aps.org/doi/10.1103/PhysRev.120.622.
- ↑ Yanase, Mutsuo M. (1961-07-15). "Optimal Measuring Apparatus" (in en). Physical Review 123 (2): 666–668. doi:10.1103/PhysRev.123.666. ISSN 0031-899X.
- ↑ Peres, Asher (1995). Concepts and Methods. Kluwer Academic Publishers. ISBN 0-7923-2549-4.
- ↑ Ghirardi, G. C.; Miglietta, F.; Rimini, A.; Weber, T. (1981-07-15). "Limitations on quantum measurements. I. Determination of the minimal amount of nonideality and identification of the optimal measuring apparatuses" (in en). Physical Review D 24 (2): 347–352. doi:10.1103/PhysRevD.24.347. ISSN 0556-2821.
- ↑ Ghirardi, G. C.; Miglietta, F.; Rimini, A.; Weber, T. (1981-07-15). "Limitations on quantum measurements. II. Analysis of a model example" (in en). Physical Review D 24 (2): 353–358. doi:10.1103/PhysRevD.24.353. ISSN 0556-2821.
- ↑ Tukiainen, Mikko (20 January 2017). "Wigner-Araki-Yanase theorem beyond conservation laws". Physical Review A 95 (1): 012127. doi:10.1103/PhysRevA.95.012127. https://journals.aps.org/pra/export/10.1103/PhysRevA.95.012127.
- ↑ Kuramochi, Yui; Tajima, Hiroyasu (2023-11-21). "Wigner-Araki-Yanase Theorem for Continuous and Unbounded Conserved Observables". Phys. Rev. Lett. 131: 210201. doi:10.1103/PhysRevLett.131.210201. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.131.210201. Retrieved 29 November 2023.
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