Uncertainty regions of observables and state-independent uncertainty relations

Abstract

The optimal state-independent lower bounds for the sum of variances or deviations of observables are of significance for the growing number of experiments that reach the uncertainty limited regime. We present a framework for computing the tight uncertainty relations of variance or deviation via determining the uncertainty regions, which are formed by the tuples of two or more of quantum observables in random quantum states induced from the uniform Haar measure on the purified states. From the analytical formulae of these uncertainty regions, we present state-independent uncertainty inequalities satisfied by the sum of variances or deviations of two, three and arbitrary many observables, from which experimentally friend entanglement detection criteria are derived for bipartite and tripartite systems.

arXiv comment42 pages; a few typoes in the published version are corrected in this version

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Cited by in corpus (5)

• Standard symmetrized variance with applications to coherence, uncertainty and entanglement
• Uncertainty relations based on state-dependent norm of commutator
• Uncertainty from the Aharonov-Vaidman Identity
• Uncertainty relation and the constrained quadratic programming
• Probability density functions of quantum mechanical observable uncertainties