A weak probe coupled to an open quantum system accumulates a finite Rényi entropy increase only when the system is in the scrambling phase, vanishing in the dissipative phase as the probe coupling goes to zero.
This choice ensures that the probe can establish extensive quantum entanglement
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Scrambling Enabled Entropy Accumulation in Open Quantum Systems
A weak probe coupled to an open quantum system accumulates a finite Rényi entropy increase only when the system is in the scrambling phase, vanishing in the dissipative phase as the probe coupling goes to zero.