Geometric formulation of the uncertainty principle
A geometric approach to formulate the uncertainty principle between quantum observables acting on an N-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a projector associated with an observable, and interpret it as the pr...
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| Autores principales: | , , , |
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| Formato: | article |
| Lenguaje: | Inglés |
| Publicado: |
2021
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| Materias: | |
| Acceso en línea: | http://hdl.handle.net/11086/20836 https://doi.org/10.1103/PhysRevA.89.034101 |
| Aporte de: |
| Sumario: | A geometric approach to formulate the uncertainty principle between quantum observables acting on an N-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a projector associated with an observable, and interpret it as the probability of obtaining the outcome corresponding to that projector. We make use of fidelity-based metrics such as angle, Bures, and root infidelity to propose a measure of uncertainty. The triangle inequality allows us to derive a family of uncertainty relations. In the case of the angle metric, we recover the Landau-Pollak inequality for pure states and show, in a natural way, how to extend it to the case of mixed states in arbitrary dimension. In addition, we derive and compare alternative uncertainty relations when using other known fidelity-based metrics. |
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