  We draw attention to the existence of "genuine" fidelity gaps in an
ancilla-assisted sequential decomposition of genuinely entangling isometry and
unitary operations of quantum computing. The gaps arise upon a bipartite
decomposition of a multiqubit operation in a one-way sequential recipe in which
an ancillary system interacts locally and only once with each qubit in a row.
Given the known "no-go" associated with such a theoretically and experimentally
desirable decomposition, various figures of merit are introduced to analyze the
optimal "fidelity" with which an arbitrary genuinely entangling operation may
admit such a sequential decomposition. An efficient variational
matrix-product-operator (VMPO) protocol is invoked in order to obtain
numerically the minimal values of the fidelity gaps incurred upon sequential
decomposition of genuine entanglers. We term the values of the gaps so obtained
genuine in the light of possible connections to the concept of the genuine
multipartite entanglement and since they are independent of the ancilla
dimension and the initial states the associated unitaries act upon.
