  Identification of possible transformations of quantum objects including
quantum states and quantum operations is indispensable in developing quantum
algorithms. Universal transformations, defined as input-independent
transformations, appear in various quantum applications. Such is the case for
universal transformations of unitary operations. However, extending these
transformations to non-unitary operations is nontrivial and largely unresolved.
Addressing this, we introduce isometry adjointation protocols that convert an
input isometry operation into its adjoint operation, which include both unitary
operation and quantum state transformations. The paper details the construction
of parallel and sequential isometry adjointation protocols, derived from
unitary inversion protocols using quantum combs, and achieving optimal
approximation error. This error is shown to be independent of the output
dimension of the isometry operation. In particular, we explicitly obtain an
asymptotically optimal parallel protocol achieving an approximation error
$\epsilon = \Theta(d^2/n)$, where $d$ is the input dimension of the isometry
operation and $n$ is the number of calls of the isometry operation. The
research also extends to isometry inversion and universal error detection,
employing semidefinite programming to assess optimal performances. The findings
suggest that the optimal performance of general protocols in isometry
adjointation and universal error detection is not dependent on the output
dimension, and that indefinite causal order protocols offer advantages over
sequential ones in isometry inversion and universal error detection.
