  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.
