Self-testing of an unbounded number of mutually commuting local observables
Sneha Munshi, A. K. Pan · Physical Review A · 2023
Based on the optimal quantum violation of the suitable Bell's inequality, device-independent self-testing of states and observables has been reported. It is well studied that locally commuting or compatible observables cannot be used to reveal quantum nonlocality. Therefore, self-testing of commuting local observables is not possible through the Bell test. In this work, we demonstrate the self-testing of a set of mutually commuting local observables. We show that the optimal quantum violations of suitably formulated bilocality and $n$-locality inequalities in networks uniquely fix the observables of one party to be mutually commuting. In particular, we first demonstrate that in a two-input arbitrary-party star network, two commuting local observables can be self-tested. Further, by considering an arbitrary-input three-party bilocal network scenario, we demonstrate the self-testing of an unbounded number of mutually commuting local observables.