Reply to M. Ziman's "Notes on optimality of direct characterization of   quantum dynamics"
  Recently M. Ziman [quant-ph/0603151] criticized our approach for quantifying the required physical resources in the theory of Direct Characterization of Quantum Dynamics (DCQD) [quant-ph/0601033, quant-ph/0601034] in comparison to other quantum process tomography (QPT) schemes. Here we argue that Ziman's comments regarding optimality, quantumness, and the novelty of DCQD are inaccurate. Specifically, we demonstrate that DCQD is optimal with respect to both the required number of experimental configurations and the number of possible outcomes over all known QPT schemes in the 2^{2n} dimensional Hilbert space of n system and n ancilla qubits. Moreover, we show DCQD is more efficient than all known QPT schemes in the sense of overall required number of quantum operations. Furthermore, we argue that DCQD is a new method for characterizing quantum dynamics and cannot be considered merely as a subclass of previously known QPT schemes. 
M. Mohseni and D. A. Lidar