In 2004, Kirkpatrick discussed three ways (I), (II) and (III) of describing non-disturbance between quantum measurements X and Y, and showed that they are all equivalent to the compatibility of X and Y if they are both sharp measurements. In 2005, based on a special sequential product on the standard effect algebra, Gudder showed that if X and Y are unsharp measurements, then (I) holds if and only if X and Y are compatible and Y is sharp measurement; compatibility of X and Y implies (II), but the converse does not hold, and only (III) is equivalent to the compatibility of X and Y. Liu and Wu (J. Phys. A, Math. Theor. 42:185206, 2009) and Shen and Wu (J. Phys. A, Math. Theor. 42:345203, 2009) showed that there are many sequential products on the standard effect algebra. In this paper, we obtain the same conclusions as Gudder’s for all these sequential products of the standard effect algebra.
展开▼
机译：2004年，柯克帕特里克（Kirkpatrick）讨论了描述量子测量X和Y之间无干扰的三种方式（I），（II）和（III），并表明如果它们都是尖锐的测量，它们都等同于X和Y的相容性。 2005年，Gudder根据标准效果代数的特殊序列乘积，得出结论：如果X和Y是不清晰的测量，则（I）当且仅当X和Y兼容且Y是清晰的测量时成立； X和Y的相容性表示（II），但相反并不成立，只有（III）等效于X和Y的相容性。Liu和Wu（J. Phys。A，Math。Theor。42：185206， 2009）和Shen and Wu（J. Phys。A，Math。Theor。42：345203，2009）表明，在标准效果代数上有许多顺序乘积。在本文中，对于标准效果代数的所有这些连续乘积，我们得出与Gudder相同的结论。
展开▼
