caa a22 4500 467905894 CHVBK 20180406152834.0 cr unu---uuuuu 170328e20060101xx s 000 0 eng 10.1007/s10701-005-9009-9 doi (NATIONALLICENCE)springer-10.1007/s10701-005-9009-9 Reconstruction of Superoperators from Incomplete Measurements [Elektronische Daten] [Mário Ziman, Martin Plesch, Vladimír zek] We present strategies how to reconstruct (estimate) properties of a quantum channel described by the map E based on incomplete measurements. In a particular case of a qubit channel a complete reconstruction of the map E can be performed via complete tomography of four output states E[ρj] that originate from a set of four linearly independent "test” states ρj (j = 1,2,3,4) at the input of the channel. We study the situation when less than four linearly independent states are transmitted via the channel and measured at the output. We present strategies how to reconstruct the channel when just one, two or three states are transmitted via the channel. In particular, we show that if just one state is transmitted via the channel then the best reconstruction can be achieved when this state is a total mixture described by the density operator ρ = I/2. To improve the reconstruction procedure one has to send via the channel more states. The best strategy is to complement the total mixture with pure states that are mutually orthogonal in the sense of the Bloch-sphere representation. We show that unitary transformations (channels) can be uniquely reconstructed (determined) based on the information of how three properly chosen input states are transformed under the action of the channel. Springer Science+Business Media, Inc., 2006 quantum dynamics nationallicence quantum process reconstruction nationallicence quantum state estimation nationallicence Ziman Mário Research Center for Quantum Information, Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 845 11, Bratislava, Slovakia aut Plesch Martin Research Center for Quantum Information, Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 845 11, Bratislava, Slovakia aut zek Vladimír Research Center for Quantum Information, Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 845 11, Bratislava, Slovakia aut Foundations of Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 36/1(2006-01-01), 127-156 0015-9018 36:1<127 2006 36 10701 https://doi.org/10.1007/s10701-005-9009-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10701-005-9009-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ziman Mário Research Center for Quantum Information, Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 845 11, Bratislava, Slovakia aut NATIONALLICENCE 700 1- Plesch Martin Research Center for Quantum Information, Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 845 11, Bratislava, Slovakia aut NATIONALLICENCE 700 1- zek Vladimír Research Center for Quantum Information, Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 845 11, Bratislava, Slovakia aut NATIONALLICENCE 773 0- Foundations of Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 36/1(2006-01-01), 127-156 0015-9018 36:1<127 2006 36 10701 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer