Necessary condition for incompatibility of observables in general probabilistic theories



: Filippov SN, Heinosaari T, Leppajarvi L

Publisher: AMER PHYSICAL SOC

: 2017

: Physical Review A

: PHYSICAL REVIEW A

: PHYS REV A

: ARTN 032127

: 95

: 3

: 8

: 2469-9926

: 2469-9934

DOI: https://doi.org/10.1103/PhysRevA.95.032127

: https://research.utu.fi/converis/portal/detail/Publication/22377757


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.

Last updated on 2024-26-11 at 13:00