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Unital Kadison-Schwarz Maps
Hajir Al Zadjali, Farrukh Mukhamedov·September 19, 2025·DOI: 10.1142/S1230161225500076
Quantum PhysicsMathematical Physics
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Abstract
Quantum entanglement is an important phenomenon in quantum information theory. To detect entanglement theoretically, positive but not completely positive maps are used. The Kadison-Schwarz (KS) inequality interpolates between positivity and complete positivity. KS maps may be key to understanding and detecting entanglement. We provide a description of a subset of KS maps on $M_2(\mathbb{C})$ that are unital. This allows for the classification of a wider class of positive maps than the well known bistochastic maps. We derive the conditions for a unital map to be a KS map, and provide non-trivial examples of such a map.