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Paper IPM / P / 13458  


Abstract:  
We draw attention to the existence of âgenuineâ fidelity gaps in an ancillaassisted 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 oneway sequential recipe in which an ancillary system interacts
locally and only once with each qubit in a row. Given the known ânogoâ associated with such a theoretically and
experimentally desirable decomposition, various figures of merit are introduced to analyze the optimal âfidelityâ
with which an arbitrary genuinely entangling operation may admit such a sequential decomposition. An efficient
variational matrixproductoperator 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 âgenuineâ 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.
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