Extremal Steering Assemblages
Thomas Cope, Tobias J. Osborne
TL;DR
This paper characterizes extremal points of quantum assemblages, providing necessary and sufficient conditions for extremality and an algorithm for decomposition, with practical implementation details.
Contribution
It introduces a complete set of conditions for extremality of assemblages and offers an algorithm to decompose any assemblage into extremal components.
Findings
Derived linear independence conditions for extremality.
Developed an algorithm for assemblage decomposition.
Provided a Matlab implementation for practical use.
Abstract
Non-local correlations between a fully characterised quantum system and an untrusted black box device are described by an assemblage of conditional quantum states. These assemblages form a convex set, whose extremal points are relevant in many operational contexts. We give necessary and sufficient conditions for an assemblage to be extremal using linear independence conditions, and an algorithm to decompose a generic assemblage into extremal points. A Matlab implementation of this algorithm is provided in the supplementary material.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Advanced Thermodynamics and Statistical Mechanics · Quantum Information and Cryptography