Operational Test of No-Signaling and a Near-Identity Binary Channel Criterion

As a motivation, a scenario is considered in which a Weinberg-type nonlinear extension may allow violations of the no-signaling constraint, making entanglement a potential resource for operational signaling. A minimal binary model is introduced: in each run, the sender selects a binary input bit and the receiver locally records a binary output bit. Signaling is defined operationally as a dependence of the local output statistics on the remote input and is summarized by a single channel parameter estimable from data. An estimator and a robust confidence interval are constructed to test the absence of signaling, and transmission reliability is quantified via the minimum decision error. Finally, a conservative criterion is proposed, based on an upper bound on the error and a threshold fixed a priori, to quantify a near-identity channel regime, together with minimal reporting requirements to rule out artifacts and classical leakage.