State independent uncertainty relations from eigenvalue minimization
arXiv:1810.09775 · doi:10.1103/PhysRevA.99.052121
Abstract
We consider uncertainty relations that give lower bounds to the sum of variances. Finding such lower bounds is typically complicated, and efficient procedures are known only for a handful of cases. In this paper we present procedures based on finding the ground state of appropriate Hamiltonian operators, which can make use of the many known techniques developed to this aim. To demonstrate the simplicity of the method we analyze multiple instances, both previously known and novel, that involve two or more observables, both bounded and unbounded.
arXiv comment14 pages, 3 figures
References in corpus (24)
- Quantum spin squeezing
- Quantum Chaos Triggered by Precursors of a Quantum Phase Transition: The Dicke Model
- Heisenberg's Uncertainty Principle
- Violation of local uncertainty relations as a signature of entanglement
- Stronger uncertainty relations for the sum of variances
- Simultaneous tracking of spin angle and amplitude beyond classical limits
- Uncertainty Relations for Angular Momentum
- Planar quantum squeezing and atom interferometry
- State-independent Uncertainty Relations and Entanglement Detection in Noisy Systems
- Tighter Uncertainty and Reverse Uncertainty Relations
- Experimental Demonstration of Uncertainty Relations for the Triple Components of Angular Momentum
- Why Two Qubits Are Special
- Tight state-independent uncertainty relations for qubits
- A Stronger Multi-observable Uncertainty Relation
- Weighted Uncertainty Relations
- Uncertainty relations for general unitary operators
- Exact uncertainty approach in quantum mechanics and quantum gravity
- Characterization of quantum angular-momentum fluctuations via principal components
- Planar squeezing by quantum non-demolition measurement in cold atomic ensembles
- State-independent preparation uncertainty relations
- Entanglement, number fluctuations and optimized interferometric phase measurement
- Experimental investigation of multi-observable uncertainty relations
- SU(2) uncertainty limits
- Uncertainty relations and joint numerical ranges
Cited by in corpus (9)
- Uncertainty relations from graph theory
- Improving sum uncertainty relations with the quantum Fisher information
- Experimental Test of Tight State-Independent Preparation Uncertainty Relations for Qubits
- Uncertainty regions of observables and state-independent uncertainty relations
- Uncertainty from the Aharonov-Vaidman Identity
- Tight bounds from multiple-observable entropic uncertainty relations
- Probability density functions of quantum mechanical observable uncertainties
- Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems
- Sequences of lower bounds for entropic uncertainty relations from bistochastic maps