Hidden Non n-locality In Linear Networks

Abstract: We study hidden nonlocality in a linear network with independent sources. In the usual paradigm of Bell nonlocality, there are certain states which exhibit nonlocality only after the application of suitable local filtering operations, which, in turn, are some special stochastic local operations assisted with classical communication (SLOCC). In the present work, we introduce the notion of hidden non n-locality. The notion is detailed using a bilocal network. We provide instances of hidden nonbilocality and nontrilocality, where we notice quite intriguingly that nonbilocality is observed even when one of the sources distributes a mixed two-qubit separable state. Furthermore, a characterization of hidden nonbilocality is also provided in terms of the Bloch-Fano decomposition, wherein we conjecture that, to witness hidden nonbilocality, one of the two states (used by the sources) must have nonnull local Bloch vectors. Noise is inevitable in practical scenarios, which makes it imperative to study any possible method to enhance the possibility of detecting nonclassicality in the presence of noise in the network. We find that local filtering enhances the robustness to noise, which we demonstrate using bit-flip and amplitude-damping channels.