Geometry of Uncertainty Relations for Linear Combinations of Position and Momentum
arXiv:1703.06563 · doi:10.1088/1751-8121/aa9cfc
Abstract
For a quantum particle with a single degree of freedom, we derive preparational sum and product uncertainty relations satisfied by linear combinations of position and momentum observables. The state-independent bounds depend on their degree of incompatibility defined by the area of a parallelogram in an -dimensional coefficient space. Maximal incompatibility occurs if the observables give rise to regular polygons in phase space. We also conjecture a Hirschman-type uncertainty relation for N observables linear in position and momentum, generalizing the original relation which lower-bounds the sum of the position and momentum Shannon entropies of the particle.
19 pages, 2 figures. Material rearranged to match published version
References in corpus (13)
- A simple test for hidden variables in spin-1 system
- Covariance matrices and the separability problem
- Towards higher precision and operational use of optical homodyne tomograms
- Heisenberg Uncertainty Relation for Three Canonical Observables
- Stronger Schrödinger-like Uncertainty Relations
- Uncertainty relations for general unitary operators
- Tight entropic uncertainty relations for systems with dimension three to five
- Multi-observable Uncertainty Relations in Product Form of Variances
- State-independent quantum contextuality for continuous variables
- Contextuality in phase space
- Detecting entanglement of continuous variables with three mutually unbiased bases
- Measurement uncertainty relations for position and momentum: Relative entropy formulation
- Universality in Uncertainty Relations for a Quantum Particle