Device-Independent Full Network Nonlocality for Arbitrary-Party and Unbounded-Input Scenario

The nonlocality arising in a multiparty network involving multiple independent sources radically differs from the standard multipartite Bell nonlocality involving a single source. The notion of the full network nonlocality (FNN) [A. Pozas-Kerstjens et al., Full network nonlocality, Phys. Rev. Lett. 128, 010403 (2022)PRLTAO0031-900710.1103/PhysRevLett.128.010403] characterizes the quantum correlations that cannot be reproduced by a local-nonlocal model featuring one local source and the rest of nonlocal no-signaling sources. However, the demonstration of FNN was limited to bilocal and trilocal star-shaped network scenarios involving three or two dichotomic measurements for edge parties. In this Letter, we first demonstrate that a large class of prevailing network inequalities does not exhibit FNN. We then introduce an elegant set of arbitrary-party and unbounded-input network inequalities in star-shaped and linear-chain networks whose optimal quantum violation exhibits FNN, certifying that the nonlocality is genuinely distributed to the entire network. Contrasting to existing demonstrations of FNN that inevitably require fixed-input and four-output elegant joint measurements for the central party, our generalized inequalities are more experimentally friendly, requiring only two output measurements. Moreover, our derivation of optimal quantum violation is fully analytic and devoid of assuming the dimension of the quantum system, thereby showcasing its potential for device-independent self-testing.