Variance uncertainty relations without covariances for three and four observables

Abstract

New sum and product uncertainty relations, containing variances of three or four observables, but not containing explicitly their covariances, are derived. One of consequences is the new inequality, giving a nonzero lower bound for the product of two variances in the case of zero mean value of the commutator between the related operators. Moreover, explicit examples show that in some cases this new bound can be better than the known Robertson--Schrödinger one.

6 pages, submitted to PRA

References in corpus (11)

• Stronger uncertainty relations for the sum of variances
• Multimode uncertainty relations and separability of continuous variable states
• Uncertainty inequalities as entanglement criteria for negative partial-transpose states
• Heisenberg Uncertainty Relation for Three Canonical Observables
• Characterization of quantum angular-momentum fluctuations via principal components
• Variance-based uncertainty relations for incompatible observables
• Multi-observable Uncertainty Relations in Product Form of Variances
• Entanglement condition via su(2) and su(1,1) algebra using Schr{ö}dinger-Robertson uncertainty relation
• Implications and applications of the variance-based uncertainty equalities
• Inseparability Criterion Using Higher-Order Schrödinger-Robertson Uncertainty Relation
• Refinement of Uncertainty Relations in Quantum Mechanics

Cited by in corpus (10)

• Continuous-variable entropic uncertainty relations
• Tight $N$-observable uncertainty relations and their experimental demonstrations
• Mutually Unbiased Coarse-Grained Measurements of Two or More Phase-Space Variables
• Experimental investigation of the uncertainty relations with coherent light
• Uncertainty relations for the support of quantum states
• Uncertainty from the Aharonov-Vaidman Identity
• Multiparticle Entanglement Resolution Analyzer based on Quantum-Control-Assisted Uncertainty Relation
• Identifying the $3$-qubit $W$ state with quantum uncertainty relation
• Multi-Operator Quantum Uncertainty Relations from New Cauchy-Schwarz Inequalities
• Spin coherence scale: operator-ordering sensitivity beyond the Heisenberg-Weyl group