Scrambling and synchronization in a monitored chaotic quantum kicked top

In this article, we study seed-dependent synchronization in a monitored quantum kicked top. The model is driven by a bounded seed waveform and conditioned on a public signal derived from a fixed spin observable. Our numerical results indicate that, for intermediate monitoring strengths, the same public conditioning record can contract a seed-compatible response while leaving a microscopically seed-shifted response transversely unstable. The diagnostic signature is a split in finite-time conditional transverse exponents: the Alice–Bob branch and a correct-seed control branch have negative exponents, whereas the wrong-seed branch has a positive exponent over the same monitoring window. We refer to this regime as a seed-selective synchronization filter. Within the simulated parameter range, the effect appears over a finite region of the ( K , η ) plane, persists across the accessible sequence of Hilbert-space sizes studied here, and is more pronounced in the more strongly scrambling parameter regime. Direct late-time trace distances and ensemble-based statistics give the same qualitative separation between synchronized and seed-mismatched branches. The results should be read as finite-time, finite-size numerical evidence for a monitored-chaotic mechanism in which a small seed mismatch is converted into persistent desynchronization, rather than as a universal stability theorem or a claim of information-theoretic security.