Let $\mathcal{A} =\{\mathsf{Q}_n\}$ be a quantum circuit, taking $n$ input qubits to $n$ output qubits. It is known that \begin{equation} \mathsf{Post}\mathcal{A} = \mathsf{Post}\mathsf{BQP}, \end{equation} where $\mathsf{Post}\mathsf{BQP}$ is defined here.

Without losing any generality, could I say that the output register of every circuit in $\mathsf{Post}\mathcal{A}$ is a single qubit, and the post-selection register of every circuit in $\mathsf{Post}\mathcal{A}$ has $(n-1)$ qubits?

Note that the output register is always a single qubit, but it wasn't immediately clear to me how much we can tweak the size of the post-selection register.



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