Chaos-controlled switching between entanglement and coherence

Controlling entanglement and coherence is central to quantum information, yet the two resources often exhibit antagonistic trends and are difficult to optimize within a single platform. Here we show that chaos enables switchable eigenstate resources: avoided crossings in soft- versus strong- chaos windows selectively realize an entanglement-peak mode or a coherence-peak mode within the same system. Crucially, this chaos-controlled inversion is not tied to a particular notion of subsystems, appearing both in single-wave settings and in genuine many-body settings. From the quantum-chaos perspective, conventional diagnostics based on avoided-crossing phenomenology and eigenmode delocalization are insufficient; eigenfunction entanglement and basis coherence provide the missing discriminants. Using two wave-chaotic billiards and a tilted-field Ising chain, we track the information-theoretic response of eigenstates across localized hybridization windows. Even when avoided-crossing phenomenology and delocalization are comparable, the entanglement and coherence responses invert between soft- and strong-chaos regimes. In the Ising chain, a single microscopic knob, the global field tilt, toggles between the two operating modes and reveals a trade-off in which off-diagonal correlations grow as diagonal populations dip. Our diagnostics require only reduced states (or their spectra) and are compatible with mode imaging in wave-chaos resonators and randomized measurements in programmable spin simulators.