Role of measurement incompatibility and state disturbance in sequential sharing of tripartite nonlocality
Phys. Rev. A 114, 032211 – Published 17 September, 2026
DOI: https://doi.org/10.1103/zpqj-2gg2
Abstract
Quantum measurements inevitably disturb the state being measured and this disturbance, together with measurement incompatibility, plays a crucial role in the sequential sharing of nonlocality. While the information-disturbance trade-off for a single measurement is well understood, its interplay with measurement incompatibility remains relatively unexplored. Here, we investigate this interplay in the sequential sharing of three forms of tripartite nonlocality: standard, genuine, and no-signaling genuine. By deriving incompatibility trade-off relations among the measurements performed by the three observers, we show that the role of measurement incompatibility differs qualitatively across three forms of nonlocality. Standard tripartite nonlocality can be demonstrated even when one party performs compatible measurements, rendering unbounded sequential sharing essentially trivial. In contrast, genuine tripartite nonlocality cannot be realized when any two parties perform nearly compatible measurements, precluding unbounded sharing. For no-signaling–genuine nonlocality, however, the incompatibility trade-off allows the critical measurement unsharpness to be arbitrarily small, along with another party's measurement to be almost compatible, so that the minimum measurement-induced disturbance required to demonstrate nonlocality can also be made arbitrarily small, preserving sufficient quantum correlations for unbounded sequential sharing. We further show that in this regime, the feasibility of unbounded sequential sharing depends sensitively on the Kraus realization implementing the measurement. Our results demonstrate that measurement incompatibility alone does not fully determine the limits of sequential multipartite nonlocality; instead, the minimum measurement-induced disturbance required to achieve nonlocality plays an equally decisive operational role.
