On the Alberti-Uhlmann Condition for Unital Channels

Sagnik Chakraborty1, Dariusz Chruściński1, Gniewomir Sarbicki1, and Frederik vom Ende2,3

1Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziądzka 5/7, 87-100 Toruń, Poland
2Department of Chemistry, Technische Universität München, 85747 Garching, Germany
3Munich Centre for Quantum Science and Technology (MCQST), Schellingstr. 4, 80799 München, Germany

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We address the problem of existence of completely positive trace preserving (CPTP) maps between two sets of density matrices. We refine the result of Alberti and Uhlmann and derive a necessary and sufficient condition for the existence of a unital channel between two pairs of qubit states which ultimately boils down to three simple inequalities.

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Cited by

[1] Katarzyna Siudzińska, Sagnik Chakraborty, and Dariusz Chruściński, "Interpolating between Positive and Completely Positive Maps: A New Hierarchy of Entangled States", Entropy 23 5, 625 (2021).

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