Chaos-controlled switching between entanglement and coherence

TL;DR

The paper investigates how chaotic dynamics can serve as a universal switch between two quantum resources: entanglement and coherence. By analyzing two wave-chaotic billiards and a tilted-field Ising chain, it shows that avoided crossings can induce entanglement-peak or coherence-peak operating modes within the same system, depending on the chaos window (soft vs strong) and the chosen subsystem partition. The study introduces a TPS-robust framework that uses Schmidt-spectrum reshuffling, reduced-state coherence via $C_d$, and purity-channel decomposition to disentangle entanglement from coherence reshaping, including a perturbative sign rule linking Schmidt weights to entropy changes. The results reveal a fundamental resource trade-off controlled by a single microscopic knob, with practical implications for task-oriented quantum state engineering in wave-chaos devices and programmable spin simulators, even in highly mixed environments.

Abstract

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.

Figures (7)

• Figure 1: Avoided crossings and configuration-space Shannon entropy in quadrupole and oval billiards. (a,b) Quadrupole: two branches form an avoided crossing as $\kappa$ is varied; representative intensities show mode exchange, while the configuration-space Shannon entropy peaks in the hybridization window. (c,d) Oval: the same analysis versus $\varepsilon$, again showing mode exchange and a Shannon-entropy peak despite stronger background mixing.
• Figure 2: Schmidt-spectrum reshuffling and entanglement inversion across avoided crossings. (a--c) Quadrupole: the leading Schmidt weights flatten across the avoided crossing, producing an entropy peak. (d--f) Oval: the leading Schmidt weights concentrate across the avoided crossing, producing an entropy dip. The reference threshold $\lambda_c=1/e$ highlights whether hybridization promotes subdominant weights (equalization) or sharpens the leading sector (concentration). Across the shown window, the leading five weights typically sum to $>0.99$, so rank-5 already captures the relevant reshuffling.
• Figure 3: Quadrupole billiard: reduced-density textures, coherence, and purity across an avoided crossing. Reduced matrices retain strong off-diagonal texture, yet $C_d^{x,y}$ and the purity dip in the hybridization window. Channel-resolved purity shows that substantial off-diagonal weight persists, indicating an entanglement-driven rebalancing rather than a trivial loss of off-diagonal structure.
• Figure 4: Oval billiard: the same diagnostics as Fig. \ref{['Figure-3']} with an inverted response. Despite similarly strong off-diagonal texture, $C_d^{x,y}$ and the purity peak in the hybridization window, consistent with the entanglement dip in Fig. \ref{['Figure-2']}(f). Off-diagonal dominance persists, so the coherence peak reflects a genuine reorganization of correlations rather than a transition to a purely diagonal reduced state.
• Figure 5: Ising chain: avoided crossings and computational-basis delocalization. (a,b) Soft-chaos window near $\theta\simeq 0.45$: an avoided crossing produces rapid basis reshuffling and a localized peak in the configuration-space Shannon entropy. (c,d) Strong-chaos window near $\theta\simeq 1.57$: baseline delocalization is already high and the avoided-crossing response becomes branch dependent (peak versus dip).