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We study the possibility for a global unitary applied on an arbitrary numberof qubits to be decomposed in a sequential unitary procedure, where anancillary system is allowed to interact only once with each qubit. We provethat sequential unitary decompositions are in general impossible for genuineentangling operations, even with an infinite-dimensional ancilla, being thecontrolled-NOT gate a paradigmatic example. Nevertheless, we find particularnontrivial operations in quantum information that can be performed in asequential unitary manner, as is the case of quantum error correction andquantum cloning.

Sequential Implementation of Global Quantum Operations