Reconstruction of Superoperators from Incomplete Measurements |
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Authors: | Mário Ziman Martin Plesch Vladimír Buž zek |
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Institution: | (1) Research Center for Quantum Information, Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 845 11 Bratislava, Slovakia;(2) Faculty of Informatics, Masaryk University, Botanická 68a, 602 00 Brno, Czech Republic;(3) Quniverse, Líščie údolie 116, 841 04 Bratislava, Slovakia;(4) Abteilung für Quantenphysik, Universität Ulm, 89069 Ulm, Germany |
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Abstract: | 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 Eρj] 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.We have originally dedicated this paper to Asher Peres on the occasion of his 70th birthday. Unfortunately, since the submission of the paper for publication Asher Peres passed away so we dedicate this paper to his memory. |
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Keywords: | quantum dynamics quantum process reconstruction quantum state estimation |
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