PSISHIFT-Eva: Probing the No-Communication Theorem via Weinberg Nonlinear QM - A Quantum Signaling Testbed with Real QPU Integration

This paper presents a testbed protocol for probing whether Weinberg (1989) nonlinear corrections to quantum mechanics produce measurable statistical asymmetries in Bell-pair measurements on real quantum hardware. The protocol prepares maximally entangled Bell states |Φ+⟩ = (|00⟩ + |11⟩)/√2, applies nonlinear Schrödinger equation (NLSE) self-phase modulation (α_ij → α_ij · exp(-i·ε·|α_ij|²)) to the four-dimensional amplitude vector, and tests whether Alice's local basis choice creates a statistically detectable bias in Bob's marginal probabilities — a signature that would constitute a violation of the no-communication theorem if observed on physical hardware. The corrected v2.0 protocol eliminates all classical side-channels present in the initial implementation. Bob's measurement probabilities derive solely from the partial trace over post-NLSE-evolution amplitudes; the bobBiasShift parameter is hardcoded to zero. Bob operates as a process-isolated OS worker (separate PID, zero shared memory, IPC-only communication) with cryptographic proof of separation. The simulator produces exactly 50% accuracy across all experimental modes (Weinberg, control, blinded), confirming the no-signaling theorem holds for the mathematical model. Preliminary hardware results from dual-IonQ trapped-ion backends yield 60% basis-inference accuracy over 40,960 measurements across 5 experimental rounds (p = 0.31), insufficient for statistical significance. A three-phase experimental roadmap is described, scaling from $10K to $2M+, incorporating spacelike separation, independent circuit generation, and atomic-clock synchronization for definitive tests. Includes full mathematical framework, dynamic epsilon evolution algorithm, experimental validation engine architecture (3 modes with z-test, chi-squared, Wilson CI, Cohen's h statistical analysis), honest disclosure of circularity limitations, and hardware integration details for IBM Quantum and IonQ backends.