Causal Coherence in Quantum Networks: Transport Laws, Superposed Structures, and Environmental Recording

What limits quantum coherence on a causal network: distance, noise, or the act of recording which structure was taken? This two-paper study develops a unified framework for answering that question. The first paper proves a general spacetime law for coherence transport in quantum networks. It separates three physically distinct effects: finite-speed causal propagation, contraction of pre-existing coherence by a quantum channel, and long-range coherence injected by non-local structural changes. The resulting bound reveals two unavoidable regimes: an early-time decay law for coherence prepared across large separations, followed by a spatial coherence envelope once the corresponding causal depth has been reached. The second paper turns to a different regime in which the network structure itself is coherently controlled. It proves that two alternative structures remain perfectly indistinguishable until quantum matter acquires amplitude in the region where they differ. More generally, it derives causal bounds on visibility loss, structure–matter entanglement, and the optimal probability of determining which structure was present. Numerical network-walk experiments illustrate exact causal protection, coherent visibility revivals, and the suppression of those revivals when environmental records are introduced. Together, the papers distinguish structural difference from irreversible decoherence: non-locality or alternative geometry alone need not destroy coherence. The decisive mechanism is whether information distinguishing the alternatives is physically acquired and irreversibly recorded. Included works:A General Causal Coherence Transport Law and Causal Protection of Coherently Superposed Network Structures.