부산대학교 도서관

Summary: ``Standard quantum tomography of a single qudit achieves aninfidelity that scales in the worst case as $O(1/\sqrt N)$ for a sampleof size $N$. Here, we propose a suitable generalization of thetwo-stage adaptive quantum tomography for a qubit to the case of asingle 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 themethod. This result is based on a second-order Taylor series expansionof the infidelity that is obtained by means of the Fréchet derivativeand measurement outcomes modeled by a multinomial distribution.Numerical simulations indicate that the choice $N_0=N/2$ leads to aninfidelity that scales approximately as $O(1/N)$ for all quantum statesin a wide range of dimensions, that is, a quadratic improvement of theinfidelity when compared to standard quantum tomography in the case oflow-rank states.''