Wu Junde

A uniqueness problem of the sequence product on operator effect algebra {\cal E}(H)

A quantum effect is an operator on a complex Hilbert space H that satisfies 0 ≤ A ≤ I. We denote the set of all quantum effects by . In this paper we prove theorem 4.3, the theory of the sequential product on which shows, in fact, that there are sequential products on which are not of the generalized Luders form. This result answers Gudders open problem negatively.

Fixed points of commutative Lüders operations

This paper verifies a conjecture posed in a pair of papers on the fixed point sets for a class of quantum operations. Specifically, it is proved that if a quantum operation has mutually commuting operation elements that are effects forming a resolution of the identity, then the fixed point set of the quantum operation is exactly the commutant of the operation elements.

Sequential product on standard effect algebra {\cal E} (H)

A quantum effect is an operator A on a complex Hilbert space H that satisfies is the set of all quantum effects on H. In 2001, Professors Gudder and Nagy studied the sequential product for . In 2005, Professor Gudder asked: Is the only sequential product on ? Recently, Liu and Wu have presented an example to show that the answer is negative. In this paper, first, we characterize some algebraic properties of the abstract sequential product on , second, we present a general method for constructing sequential products on and, finally, we study some properties of the sequential products constructed by the method.

A representation theorem of infimum of bounded quantum observables

In 2006, Gudder introduced a logic order on the bounded quantum observable set S(H). In 2007, Pulmannova and Vincekova proved that for each subset D of S(H), the infimum of D exists with respect to this logic order. In this paper, we present a representation theorem for the infimum of D.

On fixed points of Lüders operation

In this paper, we give a concrete example of a Luders operation LA with n=3, such that LA(B)=B does not imply that B commutes with all E1, E2, and E3 in A, this example answers an open problem of Professor Gudder.

On supremum of bounded quantum observable

In this paper, we present a new, necessary, and sufficient condition for which the supremum A∨B exists with respect to the logic order ≼. Moreover, we give out a new and much simpler representation of A∨B with respect to ≼. Our results have nice physical meanings.

The Brooks-Jewett Theorem on Effect Algebras with the Sequential Completeness Property

In this paper, we show that the Brooks-Jewett theorem on effect algebras with the sequential completeness property is valid.

Continuity of Effect Algebra Operations in the Interval Topology

We study the continuity of ⊕ and ⊖ of effect algebras in the interval topology, and present several examples of effect algebras with interesting properties.

On Antosik’s Lemma and the Antosik-Mikusinski Basic Matrix Theorem

That Antosiks Lemma is not a special case of the Antosik-Mikusinski Basic Matrix Theorem will be shown and, an equivalent form of the Antosik-Mikusinski Basic Matrix Theorem will also be presented in this paper.

Mutual Information and Relative Entropy of Sequential Effect Algebras

In this paper, we introduce and investigate the mutual information and relative entropy on the sequential effect algebra, we also give a comparison of these mutual information and relative entropy with the classical ones by the venn diagrams. Finally, a nice example shows that the entropies of sequential effect algebra depend extremely on the order of its sequential product.