A tensor norm approach to quantum compatibility

TL;DR

This paper explores quantum measurement incompatibility and its quantification through noise robustness, employing tensor norms and free spectrahedra to bridge quantum information theory and Banach space theory.

Contribution

It introduces a tensor norm framework for analyzing measurement incompatibility, making recent results more accessible and connecting quantum physics with Banach space theory.

Findings

Maximal noise robustness of incompatible measurements derived using tensor norms.

Reformulation of incompatibility witnesses via tensor norm and matrix convex set duality.

Enhanced understanding of measurement incompatibility through mathematical tools.

Abstract

Measurement incompatibility is one of the most striking examples of how quantum physics is different from classical physics. Two measurements are incompatible if they cannot arise via classical post-processing from a third one. A natural way to quantify incompatibility is in terms of noise robustness. In the present article, we review recent results on the maximal noise robustness of incompatible measurements, which have been obtained by the present authors using free spectrahedra, and rederive them using tensor norms. In this way, we make them accessible to a broader audience from quantum information theory and mathematical physics and contribute to the fruitful interactions between Banach space theory and quantum information theory. We also describe incompatibility witnesses using tensor norm and matrix convex set duality, emphasizing the relation between the different notions of witnesses.