arXiv subjects
Publications and source records attributed to Liu Weihua.
In this paper, we show that those sequential products which were proposed by Liu and Shen and Wu in [J. Phys. A: Math. Theor. {\bf 42}, 185206 (2009), J. Phys. A: Math. Theor. {\bf 42}, 345203 (2009)] are just unitary equivalent to the sequential product $A\circ B=A^{\frac{1}{2}}BA^{\frac{1}{2}}$.
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 points set of the quantum operation is exactly the commutant of the operation elements.
In this paper, we prove that if $\mathcal{A}=\{E_i\}_{i=1}^{n}$ is a finite commutative quantum measurement, then the fixed points set of Lüders operation $L_{\cal A}$ is the commutant ${\cal A}'$ of ${\cal A}$, the result answers an open problem partially. We also give a concrete example of a Lüders operation $L_{\cal A}$ with $n=3$ such that $L_{\cal A}(B)=B$ does not imply that the quantum effect $B$ commutes with all $E_1, E_2$ and $E_3$, this example answers another open problem.
In this paper, we present a new necessary and sufficient condition for which the supremum exists with respect to the logic order. Moreover, we give out a new and much simpler representation of the supremum with respect to the order, our results have nice physical meanings.
A quantum effect is an operator on a complex Hilbert space $H$ that satisfies $0\leq A\leq I$. We denote the set of all quantum effects by ${\cal E}(H)$. In this paper we prove, Theorem 4.3, on the theory of sequential product on ${\cal E}(H)$ which shows, in fact, that there are sequential products on ${\cal E}(H)$ which are not of the generalized Lüders form. This result answers a Gudder's open problem negatively.