A Minimal Operational Criterion for No-Signaling Assessment and Near-Identity Binary Transmission

Possible violations of the no-signaling constraint in Weinberg-type nonlinear extensions motivate the question of whether entanglement could, under suitable conditions, become a resource for operational signaling. A minimal binary model is introduced in which, in each run, a sender selects a binary input bit and a 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 that can be estimated from data. An estimator and a corrected confidence interval are then introduced to assess this dependence quantitatively, while transmission reliability is expressed through the minimum decision error. On this basis, a conservative criterion is formulated, using an upper bound on the error and a threshold fixed in advance, to characterize a near-identity channel regime. Minimal reporting requirements are also proposed to document the conditions under which artifacts and classical leakage may reasonably be excluded.