In arXiv:2207.14734v2 the authors introduce the following measure and prepare channel (Equ. 2):

$$ \Psi_0(X) = E_U \Bigl[ \sum_{j=1}^d \langle j | U^\dagger X U |j\rangle U |j \rangle \langle j | U^\dagger \Bigr] $$

Implementing this on a quantum computer (or e.g. Qiskit) would require applying $U^\dagger$ on a specified number of qubits first, then measure and then apply $U$ on the resulting state. This is also exactly what they sketch in Fig. 1. However, having a look on their pseudo code in Alg. 1 in the appendix, line 5-7 applies $U^\dagger$ only once before the measurement, but not after the measurement. Is this a typo or do I understand something wrong?



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