The Potential Imprint of Bipartite Correlation in Single-Party Statistics: From Reduced Density Matrix to ΔP≠0 in the ITC Framework

In standard quantum mechanics, Bob's single-party probability distribution is completely determined by the reduced density matrix ρB=TrA(|Ψ⟩⟨Ψ|). For the two distinct entangled states |Ψ+⟩ and |Φ+⟩, although their bipartite correlations are completely different (one always opposite, the other always identical), the partial trace operation loses all correlation information, resulting in identical ρB (both I/2). Therefore, from the perspective of Bob's single-party measurement results, the two states are indistinguishable. This paper points out that the ITC framework introduces a basal structure, where P1 (Storage Perfection) and P2 (Instantaneous Connectivity) make it possible for the difference in bipartite correlations to leave an "imprint" in Bob's single-party statistical data. This imprint manifests as a tiny shift ΔP≠0 in Bob's single-party probability before and after modulation, thus providing a testable theoretical foundation for superluminal communication.