On Fixed Points of Lüders Operation

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 $L_{\mathcal{A}}$ is the commutant ${\mathcal{A}}^{\prime }$ of $\mathcal{A}$, the result answers an open problem partially. We also give a concrete example of a Lüders operation $L_{\mathcal{A}}$ with $n=3$ such that $L_{\mathcal{A}}(B)=B$ does not imply that the quantum effect $B$ commutes with all $E_1,E_2$ and $E_3$, this example answers another open problem.

References in corpus (1)

• Lüders Theorem for Unsharp Quantum Measurements

Cited by in corpus (6)

• Non-disturbing quantum measurements
• Fixed points of commutative Lüders operations
• Measurement disturbance and conservation laws in quantum mechanics
• The Continuity of Sequential Product of Sequential Quantum Effect Algebras
• Structural Characterization And Condition For Measurement Statistics Preservation Of A Unital Quantum Operation
• The n-th root of sequential effect algebras