A simple formula for the average gate fidelity of a quantum dynamical   operation
  This note presents a simple formula for the average fidelity between a unitary quantum gate and a general quantum operation on a qudit, generalizing the formula for qubits found by Bowdrey et al [Phys. Lett. A 294, 258 (2002)]. This formula may be useful for experimental determination of average gate fidelity. We also give a simplified proof of a formula due to Horodecki et al [Phys. Rev. A 60, 1888 (1999)], connecting average gate fidelity to entanglement fidelity. 
Michael A. Nielsen