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.
Keywords
Cite
@article{arxiv.2110.14134,
title = {Uncertainty regions of observables and state-independent uncertainty relations},
author = {Lin Zhang and Shunlong Luo and Shao-Ming Fei and Junde Wu},
journal= {arXiv preprint arXiv:2110.14134},
year = {2021}
}
Comments
42 pages; a few typoes in the published version are corrected in this version