Controlled-Memory Identification with Shared Generators: Dimension--Horizon Tradeoffs and Quantum--Classical Separation
The research investigates how long prefix and query words must be for a fixed number of shared control generators to identify a memory's state. It finds that four shared generators allow identification sizes to reach static code-size limits in optimal word lengths, showing a quadratic quantum-classical separation. This means four letters are enough to achieve these bounds in both quantum and classical settings.