{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
BT - Phys. Rev. A DO - 10.1103/PhysRevA.92.032109 LA - eng N2 -{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
PY - 2015 EP - 032109 T2 - Phys. Rev. A TI - Certainty relations, mutual entanglement and non-displacable manifolds UR - https://doi.org/10.1103/PhysRevA.92.032109 VL - 92 ER -