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 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.
| Main Authors: | , , , |
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| Format: | article biblioteca |
| Language: | eng |
| Published: |
2014
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| Subjects: | Uncertainty principle, Landau-Pollak inequality, Fidelity-based metrics, Quantum distances, |
| Online Access: | http://hdl.handle.net/11086/20836 https://doi.org/10.1103/PhysRevA.89.034101 |
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