量子效应的分解

Factorizations of quantum effects

研究了Hilbert空间上一个量子效应分解成几个sharp量子效应和almost sharp量子效应之和的问题.得到了一个量子效应是sharp效应与almost sharp效应之和的充要条件及是两个sharp效应之和的充要条件,给出了一个效应是almost sharp效应的充要条件.作为应用,证明了当H的维数是无限的或者维数是偶数时,一个量子效应可以分解成两个almost sharp量子效应之和;当H的维数是奇数时,一个量子效应可以分解成至多三个almost sharp量子效应之和.

Some necessary and sufficient conditions are established respectively for an effect to be a sum of a sharp effect and an almost sharp effect, and to be a sum of two sharp effects. A necessary and sufficient condition is also given for an effect to be almost sharp. As applications, an effect can be represented as a sum of two almost sharp effects if the dimension of H is infinite or even and as a sum of at most three sharp effects if the dimension of H is odd.