The interference degree between two measurable sets with respect to a quantum measure
HU Kaifeng, GUO Zhihua, CAO Huaixin*
(School of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710119, Shaanxi, China)
Abstract:
Based on a discussion of some properties of a quantum measure, the new concept of the interference degree of two measurable sets with respect to a quantum measure is introduce, and its properties are investigated.It is proved that any quantum measurement is n(≥3) level additive and the interference of a measure-zero set between a measurable set that does not intersect the former is zero. It is also proved that a quantum measure gives zero-interference everywhere if and only if it is finitely additive and a continuous quantum measure gives zero-interference everywhere if and only if it is a classical measure, i.e. countably additive.The interference degree of a subset of measure-zero set and any measurable set that does not intersect the former is discussed.
KeyWords:
quantum measure; measurable set; interference degree
