2018/07/31 by Andreas Blühm, Andreas Bluhm, Ion Nechita · 29 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Diamond #Joint (building) #Materials science #Mathematics #Matrix (chemical analysis) #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Statistical physics #math-ph #math.MP #math.OA #quant-ph
paper · pdf · doi:10.1063/1.5049125
published in Journal of Mathematical Physics 59(11) (American Institute of Physics) · 28 pages, 4 figures. v3: minor revisions
arxiv created 2018/09/26 · openalex publication_date 2018/11/01 · arxiv updated 2019/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
In this work, we investigate the joint measurability of quantum effects and connect it to the study of free spectrahedra. Free spectrahedra typically arise as matricial relaxations of linear matrix inequalities. An example of a free spectrahedron is the matrix diamond, which is a matricial relaxation of the ℓ1-ball. We find that joint measurability of binary positive operator valued measures is equivalent to the inclusion of the matrix diamond into the free spectrahedron defined by the effects under study. This connection allows us to use results about inclusion constants from free spectrahedra to quantify the degree of incompatibility of quantum measurements. In particular, we completely characterize the case in which the dimension is exponential in the number of measurements. Conversely, we use techniques from quantum information theory to obtain new results on spectrahedral inclusion for the matrix diamond.