Chaos-Mediated Quantum State Discrimination Near Unit Fidelity

We investigate a "quantum microscope" for qubits based on nonlinear discrete-time chaotic dynamics, which exponentially amplifies the initially small fidelity of a pair of states to a large saturation value $sim$ 1/2, thereby pushing the Helstrom bound to more accessible values. We show that Bell-type temporal correlations can capture even the minutest differences between two initial states, thus enabling their distinguishability. The cost of distinguishability is quantified in terms of the characteristic waiting time of the evolution, defined as the time after which the temporal correlation of a given initial state begins to diverge exponentially from that of a nearby state. The closer the two states are, the longer this waiting time becomes. By combining chaos with Bell-type temporal correlations, this approach opens unexplored avenues for pushing the limits of precision in quantum metrology.