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Characterizations of fixed points of quantum operations. (English) Zbl 1317.81014
Summary: Let \(\phi_{\mathcal{A}}\) be a general quantum operation. An operator \(B\) is said to be a fixed point of \(\phi_{\mathcal{A}}\), if \(\phi_{\mathcal{A}}(B)=B\). In this note, we shall show conditions under which \(B\), a fixed point \(\phi_{\mathcal{A}}\), implies that \(B\) is compatible with the operation element [the Kraus operators] of \(\phi_{\mathcal{A}}\). In particular, we offer an extension of the generalized Lüders theorem.
©2011 American Institute of Physics

MSC:
81P15 Quantum measurement theory, state operations, state preparations
46L07 Operator spaces and completely bounded maps
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