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I just wanted to double check my understanding of (26) in the following notes: https://arxiv.org/pdf/1512.08882.pdf.

Is the reason that ##(U_{T}\cdot K) \cdot (U_{C}\cdot K) = U_{T}\cdot U_{C}^{*}## because ##K## is a unitary operators and thus ##(K\cdot U_{C}\cdot K) = U_{C}^{*}## as we would expect of a unitary transformation?