A tensor norm approach to quantum compatibility
arXiv:2202.13993 · doi:10.1063/5.0089770
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.
arXiv comment18 pages, 1 figure
References in corpus (19)
- Quantum entanglement
- Bell nonlocality
- Bell Inequalities and the Separability Criterion
- An Invitation to Quantum Incompatibility
- Quantum Incompatibility Witnesses
- Noise Robustness of the Incompatibility of Quantum Measurements
- Comparing the degrees of incompatibility inherent in probabilistic physical theories
- Dilations, inclusions of matrix convex sets, and completely positive maps
- Minimal and maximal matrix convex sets
- Incompatible measurements in a class of general probabilistic theories
- Joint measurability of quantum effects and the matrix diamond
- Approximate joint measurement of qubit observables through an Arthur-Kelly type model
- Estimating the expectation values of spin 1/2 observables with finite resources
- Incompatibility in general probabilistic theories, generalized spectrahedra, and tensor norms
- Compatibility of quantum measurements and inclusion constants for the matrix jewel
- Compatibility for Probabilistic Theories
- Compact convex structure of measurements and its applications to simulability, incompatibility, and convex resource theory of continuous-outcome measurements
- Assemblages and steering in general probabilistic theories
- Maximal violation of steering inequalities and the matrix cube