Geometric approach to extend Landau-Pollak uncertainty relations for positive operator-valued measures
We provide a twofold extension of Landau-Pollak uncertainty relations for mixed quantum states and for positive operator-valued measures, by recourse to geometric considerations. The generalization is based on metrics between pure states, having the form of a function of the square of the inner prod...
Guardado en:
| Autores principales: | , , , , |
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| Formato: | article |
| Lenguaje: | Inglés |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | http://hdl.handle.net/11086/28333 https://doi.org/10.48550/arXiv.1406.3537 |
| Aporte de: |
| Sumario: | We provide a twofold extension of Landau-Pollak uncertainty relations for mixed quantum states and for positive operator-valued measures, by recourse to geometric considerations. The generalization is based on metrics between pure states, having the form of a function of the square of the inner product between the states. The triangle inequality satisfied by such metrics plays a crucial role in our derivation. The usual Landau-Pollak inequality is thus a particular case (derived from Wootters metric) of the family of inequalities obtained, and, moreover, we show that it is the most restrictive relation within the family. |
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