Entanglement-fidelity relations for inaccurate ancilla-driven quantum computation

It was shown in \[T. Morimae, Phys. Rev. A {\bf81}, 060307(R) (2010)\] that the gate fidelity of an inaccurate one-way quantum computation is upper bounded by a decreasing function of the amount of entanglement in the register. This means that a strong entanglement causes the low gate fidelity in the one-way quantum computation with inaccurate measurements. In this paper, we derive similar entanglement-fidelity relations for the inaccurate ancilla-driven quantum computation. These relations again imply that a strong entanglement in the register causes the low gate fidelity in the ancilla-driven quantum computation if the measurements on the ancilla are inaccurate.