2016/09/30 by Sergey N. Filippov, Sergey Filippov, Teiko Heinosaari +1 · 26 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Applied mathematics #Artificial intelligence #Computer science #Eigenvalues and eigenvectors #Epistemology #Mathematical economics #Mathematics #Noise (video) #Observable #Operator (biology) #Physics #Probabilistic logic #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Simple (philosophy) #Statistical physics #Statistics #Theoretical physics #quant-ph
paper · pdf · doi:10.1103/physreva.95.032127
published in Physical Review A 95(3) (American Physical Society) · Minor corrections in v2
arxiv created 2017/03/02 · openalex publication_date 2017/03/22 · arxiv updated 2017/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We quantify the intrinsic noise content of an observable in a general probabilistic theory and derive a noise content inequality for incompatible observables. We apply the derived inequality to standard quantum theory, the quantum theory of processes, and polytope state spaces. The noise content for positive operator-valued measures takes a particularly simple form and equals the sum of minimal eigenvalues of all the effects. We illustrate our findings with a number of examples including the introduced notion of reverse observables.