dorsal/arxiv
View SchemaExact uncertainty relations: technical details
| Authors | Michael J. W. Hall |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0103072 |
| URL | https://arxiv.org/abs/quant-ph/0103072 |
Abstract
The Heisenberg inequality \Delta X \Delta P \geq \hbar/2 can be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty, which is valid for all wavefunctions. The significance of this "exact" uncertainty relation is discussed, and results are generalised to angular momentum and phase, photon number and phase, time and frequency, and to states described by density operators. Connections to optimal estimation of an observable from the measurement of a second observable, Wigner functions, energy bounds, and entanglement are also given.
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"abstract": "The Heisenberg inequality \\Delta X \\Delta P \\geq \\hbar/2 can be replaced by\nan exact equality, for suitably chosen measures of position and momentum\nuncertainty, which is valid for all wavefunctions. The significance of this\n\"exact\" uncertainty relation is discussed, and results are generalised to\nangular momentum and phase, photon number and phase, time and frequency, and to\nstates described by density operators. Connections to optimal estimation of an\nobservable from the measurement of a second observable, Wigner functions,\nenergy bounds, and entanglement are also given.",
"arxiv_id": "quant-ph/0103072",
"authors": [
"Michael J. W. Hall"
],
"categories": [
"quant-ph"
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"title": "Exact uncertainty relations: technical details",
"url": "https://arxiv.org/abs/quant-ph/0103072"
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