A Stronger Multi-observable Uncertainty Relation

Abstract

Uncertainty relation lies at the heart of quantum mechanics, characterizing the incompatibility of non-commuting observables in the preparation of quantum states. An important question is how to improve the lower bound of uncertainty relation. Here we present a variance-based sum uncertainty relation for $N$ incompatible observables stronger than the simple generalization of the uncertainty relation for two observables derived by Maccone and Pati [Phys. Rev. Lett. {\bf113}, 260401 (2014)]. Further comparisons of our uncertainty relation with other related ones for spin-$\frac{1}{2}$ and spin-$1$ particles indicate that the obtained uncertainty relation gives a better lower bound.

Updated version with minor corrections

References in corpus (6)

• Heisenberg's Uncertainty Principle
• Stronger uncertainty relations for the sum of variances
• Heisenberg Uncertainty Relation for Three Canonical Observables
• Variance-based uncertainty relations for incompatible observables
• Multi-observable Uncertainty Relations in Product Form of Variances
• Implications and applications of the variance-based uncertainty equalities

Cited by in corpus (20)

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• Holevo Bound of Entropic Uncertainty in Schwarzschild Spacetime
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• Experimental investigation of multi-observable uncertainty relations
• Tighter Einstein-Podolsky-Rosen steering inequality based on the sum uncertainty relation
• Quantum uncertainty relation based on the mean deviation
• State independent uncertainty relations from eigenvalue minimization
• Tighter sum uncertainty relations via metric-adjusted skew information
• Tighter sum uncertainty relations via variance and Wigner-Yanase skew information for N incompatible observables
• State-independent Uncertainty Relations and Entanglement Detection
• Tripartite quantum-memory-assisted entropic uncertainty relations for multiple measurements
• Uncertainty relations based on Wigner-Yanase skew information
• Experimental investigation of the uncertainty relations with coherent light
• On the Weak Point of the Stronger Uncertainty Relation
• Uncertainty from the Aharonov-Vaidman Identity
• Quantum Uncertainty Equalities and Inequalities for Unitary Operators
• Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems
• Multi-Operator Quantum Uncertainty Relations from New Cauchy-Schwarz Inequalities
• A Universal Quantum Certainty Relation for Arbitrary Number of Observables