Multi-observable Uncertainty Relations in Product Form of Variances

Abstract

We investigate the product form uncertainty relations of variances for $n(n\ge 3)$ quantum observables. In particular, tight uncertainty relations satisfied by three observables has been derived, which is shown to be better than the ones derived from the strengthened Heisenberg and the generalized Schrödinger uncertainty relations, and some existing uncertainty relation for three spin-half operators. Uncertainty relation of arbitrary number of observables is also derived. As an example, the uncertainty relation satisfied by the eight Gell-Mann matrices is presented.

7 pages, 3 figures in Scientific Reports 2016

References in corpus (8)

• The uncertainty principle determines the non-locality of quantum mechanics
• Stronger uncertainty relations for the sum of variances
• Multimode uncertainty relations and separability of continuous variable states
• Improved bounds in entropic uncertainty relations
• Majorization approach to entropic uncertainty relations for coarse-grained observables
• Sum Uncertainty Relation in Quantum Theory
• Rényi entropy uncertainty relation for successive projective measurements
• Heisenberg Uncertainty Relation for Three Canonical Observables

Cited by in corpus (8)

• Experimental investigation of multi-observable uncertainty relations
• Uncertainties of genuinely incompatible triple measurements based on statistical distance
• Tighter sum uncertainty relations via variance and Wigner-Yanase skew information for N incompatible observables
• Tripartite quantum-memory-assisted entropic uncertainty relations for multiple measurements
• Uncertainty from the Aharonov-Vaidman Identity
• Optimizing incompatible triple quantum measurements
• A Universal Quantum Certainty Relation for Arbitrary Number of Observables
• Multi-Operator Quantum Uncertainty Relations from New Cauchy-Schwarz Inequalities