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We report experimental implementation of various types of qubit channelsusing an individual trapped ion. We analyzed experimental data and we performedtomographic reconstruction of quantum channels based on these data.Specifically, we studied phase damping channels, where the damping acts eitherin the xy-plane of the Bloch sphere or in an arbitrary plane that includes theorigin of the Bloch sphere. We also experimentally realized and consequentlyanalyzed quantum channels that in addition to phase damping affect also apolarization rotation. We used three reconstruction schemes for estimation ofquantum channels from experimental data: (1) a linear inverse method, (2) amaximum likelihood estimation, and (3) a constrained maximum likelihoodestimation. We took into account realistic experimental conditions whereimperfect test-state preparations and biased measurements are incorporated intothe estimation schemes. As a result we found that imperfections present in theprocess of preparation of test states and as well as in measurements of theconsidered ion trap system do not limit the control of the implementation ofthe desired channel. Even imperfect preparation of test state and subsequentmeasurements still provide sufficient resources for the completequantum-channel tomography.

Scrutinizing single-qubit quantum channels: Theory and experiment with trapped ions