2020/10/31 by Roope Uola, Tristan Kraft, Sébastien Designolle +5 · 14 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Class (philosophy) #Computer science #Dimension (graph theory) #Discrete mathematics #Linear subspace #Mathematical analysis #Mathematics #Physics #Projection (relational algebra) #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Set (abstract data type) #Subspace topology #Theoretical physics #quant-ph
paper · pdf · doi:10.1103/physreva.103.022203
published in Physical Review A 103(2) (American Physical Society) · 12 pages, no figures, comments are welcome! v2: published version
openalex publication_date 2021/02/05 · arxiv created 2021/02/26 · arxiv updated 2021/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We consider the question of characterizing the incompatibility of sets of high-dimensional quantum measurements. We introduce the concept of measurement incompatibility in subspaces. That is, starting from a set of measurements that is incompatible, one considers the set of measurements obtained by projection onto any strict subspace of fixed dimension. We identify three possible forms of incompatibility in subspaces: (i) incompressible incompatibility---measurements that become compatible in every subspace, (ii) fully compressible incompatibility---measurements that remain incompatible in every subspace, and (iii) partly compressible incompatibility---measurements that are compatible in some subspace and incompatible in another. For each class, we discuss explicit examples. Finally, we present some applications of these ideas. First, we show that joint measurability and coexistence are two inequivalent notions of incompatibility in the simplest case of qubit systems. Second, we highlight the implications of our results for tests of quantum steering.