Replica clouds: coherence and finite equal-weight quantum representations

Replica cloud theory associates the alternatives of a quantum object with one physical identity. Water motivates the possibility of unresolved structure beneath the observed packet, while contextual populations and a positive coherence matrix retain its quantum information. For a prescribed context, this article determines the leading worst-case trace-distance error of finite equal-weight representations for every fixed coherence matrix. The coefficient is set by coherence blocks joining the limiting populated support to its complement; with zero counts allowed, this coefficient is halved. Mutually incoherent groups obey a quadratic composition rule, so the worst case can approach a face containing several occupied alternatives. Fully coherent groups admit an exact finite-capacity reduction, while the binary problem gives an exact coherence-dependent crossover. For specified mixed states, a bounded integer search certifies the allocation error and can bound the remaining gap to optimality. A four-alternative analyzer realizes that error as an explicit probability difference of measurement. Standard quantum channels connect the construction to contexts and records. These results quantify the finite representation of one cloud and the accuracy requirements for a microscopic realization. “Preprint submitted to SciPost Physics on 10 September 2026. Not yet peer reviewed.”