The compatibility dimension of quantum measurements - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Mathematical Physics Année : 2021

The compatibility dimension of quantum measurements

Résumé

We introduce the notion of compatibility dimension for a set of quantum measurements: it is the largest dimension of a Hilbert space on which the given measurements are compatible. In the Schr\"odinger picture, this notion corresponds to testing compatibility with ensembles of quantum states supported on a subspace, using the incompatibility witnesses of Carmeli, Heinosaari, and Toigo. We provide several bounds for the compatibility dimension, using approximate quantum cloning or algebraic techniques inspired by quantum error correction. We analyze in detail the case of two orthonormal bases, and, in particular, that of mutually unbiased bases.

Dates et versions

hal-02988614 , version 1 (04-11-2020)

Identifiants

Citer

Faedi Loulidi, Ion Nechita. The compatibility dimension of quantum measurements. Journal of Mathematical Physics, 2021, 62 (4), pp.042205. ⟨10.1063/5.0028658⟩. ⟨hal-02988614⟩
85 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More