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 within 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 protocol is invoked in order to obtain numerically the minimal values of the fidelity gaps incurred upon the sequential decomposition of genuine entanglers. We call the values of the gaps so obtained “genuine” in light of possible connections to the concept of the genuine multipartite entanglement and since they turn out to be independent of the ancilla dimension and the initial states the associated isometries or unitaries act upon.

• Received 5 June 2013

DOI:https://doi.org/10.1103/PhysRevA.88.062315