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In his (excellent, imo) Lectures on the Mathematics of Quantum Mechanics (2015), G. Dell'Antonio writes:

"The preparation of states in Quantum Mechanics [...] is a foundational problem [...]. Very little theoretical and mathematical work has been devoted to this subject, although on the experimental side very accurate empirical procedures have been developed involving precise control of macroscopic apparatuses. This is a field in which more research would be needed".

Since $2022>2015$ and also since "very little" $\ne\emptyset$, I'm searching for some works on the subject. In a way, various no-go theorems, including the most popular one, technically fall in this category, but I'd be interested in mathematical work more closely related to the experimental protocols routinely employed in labs.

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A recent paper that also gives an overview of the topic is A new problem for quantum mechanics by A. Meehan (2020).

You may also want to look at The preparation of states in quantum mechanics by Fröhlich and Schubnel (2016).

Neither paper aims at efficient experimental implementations, for that perspective a recent paper is Quantum state preparation protocol for encoding classical data into the amplitudes of a quantum information processing register's wave function by S. Ashhab (2022).

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