Abstract
Some recent references have considered quantum detection problems in discrete and continuous frames. This paper examines the quantum detection problem with g-frame in finite dimensions. We will discuss two issues related to the problem at hand: the quantum injectivity problem and the solvability of the quantum state estimation problem. This work addresses the quantum detection problem in a broader context and provides multiple descriptions of quantum injective g-frames. Specifically, we also offer a quantitative stability outcome for g-frames.
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