Extremal quantum protocols
Giacomo Mauro D'Ariano, Paolo Perinotti, Michal Sedlak
TL;DR
This paper characterizes the extremal points of the convex set of generalized quantum instruments with finite outcomes, providing algebraic conditions for extremality in finite-dimensional quantum systems.
Contribution
It introduces algebraic necessary and sufficient conditions for identifying extremal generalized quantum instruments with finite outcomes.
Findings
Derived algebraic conditions for extremality
Characterized extremal points in finite-dimensional systems
Enhanced understanding of quantum measurement structures
Abstract
Generalized quantum instruments correspond to measurements where the input and output are either states or more generally quantum circuits. These measurements describe any quantum protocol including games, communications, and algorithms. The set of generalized quantum instruments with a given input and output structure is a convex set. Here we investigate the extremal points of this set for the case of finite dimensional quantum systems and generalized instruments with finitely many outcomes. We derive algebraic necessary and sufficient conditions for extremality.
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