Stronger Reverse Uncertainty Relation for Multiple Incompatible Observables

Abstract: Recently,D.Mondal et.al[Phys. Rev. A. 95, 052117(2017)]creatively introduce a new interesting concept of reverse uncertainty relation which indicates that one cannot only prepare quantum states with joint small uncertainty, but also with joint great uncertainty for incompatible observables. However, the uncertainty upper bound they constructed cannot express the essence of this concept well, i.e., the upper bound will go to infinity in some cases even for incompatible observables. Here, we construct a new reverse uncertainty relation and successfully fix this "infinity" problem. Also, it is found that the reverse uncertainty relation and the normal uncertainty relation are the same in essential, and they both can be unified by the same theoretical framework. Moreover, taking advantage of this unified framework, one can construct a reverse uncertainty relation for multiple observables with any tightness required. Meanwhile, the application of the new uncertainty relation in purity detection is discussed.