Certainty relations, mutual entanglement and non-displacable manifolds

Author Puchała Z.; Rudnicki Ł.; Chabuda K.; Paraniak M.; Życzkowski K.
Title Certainty relations, mutual entanglement and non-displacable manifolds
Journal Phys. Rev. A
Year 2015
Status Published
Volume 92
Pages 032109
DOI 10.1103/PhysRevA.92.032109
URL https://doi.org/10.1103/PhysRevA.92.032109
Abstract <p>{We derive explicit bounds for the average entropy characterizing measurements of a pure quantum state of size N in L orthogonal bases. Lower bounds lead to novel entropic uncertainty relations, while upper bounds allow us to formulate universal certainty relations. For L=2 the maximal average entropy saturates at logN as there exists a mutually coherent state, but certainty relations are shown to be nontrivial for L≥3 measurements. In the case of a prime power dimension</p>