Unital Kadison-Schwarz Maps

Hajir Al Zadjali; Farrukh Mukhamedov

doi:10.1142/S1230161225500076

Unital Kadison-Schwarz Maps

Hajir Al Zadjali
, Farrukh Mukhamedov

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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 M₂(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 nontrivial examples of such a map.

Original language	English
Article number	2550007
Journal	Open Systems and Information Dynamics
Volume	32
Issue number	2
DOIs	https://doi.org/10.1142/S1230161225500076
Publication status	Published - Jun 1 2025

Keywords

Kadison-Schwarz inequality
Positive maps
qubit
unital maps

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Mathematical Physics

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10.1142/S1230161225500076

Cite this

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AB - 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 M2(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 nontrivial examples of such a map.

KW - Kadison-Schwarz inequality

KW - Positive maps

KW - qubit

KW - unital maps

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Unital Kadison-Schwarz Maps

Abstract

Keywords

ASJC Scopus subject areas

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