In this paper,we introduce and investigate the mutual information and relative entropy on the sequentialeffect algebra,we also give a comparison of these mutual information and relative entropy with the classical ones...In this paper,we introduce and investigate the mutual information and relative entropy on the sequentialeffect algebra,we also give a comparison of these mutual information and relative entropy with the classical ones by thevenn diagrams.Finally,a nice example shows that the entropies of sequential effect algebra depend extremely on theorder of its sequential product.展开更多
A sequential effect algebra （E, 0, 1, ,o） is an effect algebra on which a sequential product o with certain physics properties is defined; in particular, sequential effect algebra is an important model for studying...A sequential effect algebra （E, 0, 1, ,o） is an effect algebra on which a sequential product o with certain physics properties is defined; in particular, sequential effect algebra is an important model for studying quantum measurement theory. In 2005, Gudder asked the following problem： If a, b E （E, 0, 1, , o） and a⊥b and a o b⊥a o b, is it the case that 2（a o b） ≤ a2 b2 ？ In this paper, we construct an example to answer the problem negatively.展开更多
基金Supported by Research Foundation of Kumoh National Institute of Technology
文摘In this paper,we introduce and investigate the mutual information and relative entropy on the sequentialeffect algebra,we also give a comparison of these mutual information and relative entropy with the classical ones by thevenn diagrams.Finally,a nice example shows that the entropies of sequential effect algebra depend extremely on theorder of its sequential product.
基金Supported by Natural Science Fund of China (Grant Nos. 10771191 and 10471124)
文摘A sequential effect algebra （E, 0, 1, ,o） is an effect algebra on which a sequential product o with certain physics properties is defined; in particular, sequential effect algebra is an important model for studying quantum measurement theory. In 2005, Gudder asked the following problem： If a, b E （E, 0, 1, , o） and a⊥b and a o b⊥a o b, is it the case that 2（a o b） ≤ a2 b2 ？ In this paper, we construct an example to answer the problem negatively.
