00948nas a2200181   4500000000100000000000100001008004100002100002200043700001700065700001500082700001600097700002200113245007500135856004700210300001100257490000700268520049100275       2015                            d1 aZbigniew Puchała1 aŁ. Rudnicki1 aK. Chabuda1 aM. Paraniak1 aKarol Życzkowski00aCertainty relations, mutual entanglement and non-displacable manifolds  uhttps://doi.org/10.1103/PhysRevA.92.032109  a0321090 v923 a<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>