  In a quantum computation with pure states, the generation of large amounts of
entanglement is known to be necessary for a speedup with respect to classical
computations. However, examples of quantum computations with mixed states are
known, such as the deterministic computation with one quantum qubit (DQC1)
model [Knill and Laflamme, Phys. Rev. Lett. 81, 5672 (1998)], in which
entanglement is at most marginally present, and yet a computational speedup is
believed to occur. Correlations, and not entanglement, have been identified as
a necessary ingredient for mixed-state quantum computation speedups. Here we
show that correlations, as measured through the operator Schmidt rank, are
indeed present in large amounts in the DQC1 circuit. This provides evidence for
the preclusion of efficient classical simulation of DQC1 by means of a whole
class of classical simulation algorithms, thereby reinforcing the conjecture
that DQC1 leads to a genuine quantum computational speedup.
