부산대학교 도서관

Summary: ``Standard quantum tomography of a single qudit achieves an infidelity that scales in the worst case as $O(1/\sqrt N)$ for a sample of size $N$. Here, we propose a suitable generalization of the two-stage adaptive quantum tomography for a qubit to the case of a single qudit. This achieves an infidelity of the order of $O[1/\sqrt{N_0(N-N_0)}]$ for all quantum states, where $N_0$ and $N-N_0$ are the ensemble sizes employed in the two stages of the method. This result is based on a second-order Taylor series expansion of the infidelity that is obtained by means of the Fréchet derivative and measurement outcomes modeled by a multinomial distribution. Numerical simulations indicate that the choice $N_0=N/2$ leads to an infidelity that scales approximately as $O(1/N)$ for all quantum states in a wide range of dimensions, that is, a quadratic improvement of the infidelity when compared to standard quantum tomography in the case of low-rank states.''