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arXiv · 0906.1412

On Fixed Points of Lüders Operation

Liu Weihua·Wu Junde
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Abstract

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.

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Liu Weihua, Wu Junde. 2009-09-08. On Fixed Points of Lüders Operation. https://doi.org/10.1063/1.3253574

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