Controlled-Memory Identification with Shared Generators: Dimension--Horizon Tradeoffs and Quantum--Classical Separation

arXiv:2610.21797v1 Announce Type: cross Abstract: We determine the finite-horizon identification limits of a \(d\)-dimensional memory when the control interface is restricted to four shared, time-homogeneous generators. A writer encodes a message by applying a prefix word to a common root state. The verifier then applies a candidate-dependent query word followed by a shared terminal binary test, with each word of length at most \(T\). For fixed error tolerances \(\lambda_2>0\) and \(\lambda_1+\lambda_2