Entropic Uncertainty Relation and Information Exclusion Relation for multiple measurements in the presence of quantum memory

Abstract

The Heisenberg uncertainty principle shows that no one can specify the values of the non-commuting canonically conjugated variables simultaneously. However, the uncertainty relation is usually applied to two incompatible measurements. We present tighter bounds on both entropic uncertainty relation and information exclusion relation for multiple measurements in the presence of quantum memory. As applications, three incompatible measurements on Werner state and Horodeckia € s bound entangled state are investigated in details.