Seminarium KMMF "Teoria Dwoistości"

Modern quantum devices require precise implementation of desired quantumchannels. The quality of this implementation can be characterized usingthe notion of operation fidelity, which measures the overlap betweeninitial states and their images with respect to the considered channel.I present the results of my research, conducted together with prof.Karol Życzkowski and dr Grzegorz Rajchel-Mieldzioć, where we analyze thestatistical properties of operation fidelity of low-dimensionalchannels, in particular its distributions and extremal values.First, I briefly revise the notions of fidelity between quantum statesand numerical range and shadow of a linear operator. Then, I showseveral examples of quantum channels whose operation fidelitydistributions can be calculated exactly (namely, mixed unitary qubitchannels and unitary qutrit channels). Lastly, I present a method ofanalyzing quantum channels utilizing the concepts of numerical range andshadow of their Kraus operators, using Schur channels as an example.