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We study the time evolution of entanglement in a quantum version of the Kacring. Our model consists of two spin chains and quantum gates instead of theclassical markers. The gates take one qubit from each ring at a time as aninput and entangle them. Subsequently, one ring is rotated. This protocolcreates non-trivial entanglement between the two rings, which we measure by theentanglement entropy. The features of the entanglement evolution can best beunderstood by using knowledge about the behavior of an ensemble of classicalKac rings. For instance, the recurrence time of this quantum many-body systemis twice the length of the chain and "thermalization" only occurs on timescales much smaller than the dimension of the Hilbert space. The model thuselucidates the relation between distribution of measurement results in quantumand classical systems: While in classical systems repeated measurements areperformed over an ensemble of systems, the corresponding result is obtained bymeasuring the same quantum system prepared in an appropriate superpositionrepeatedly.

Entanglement propagation and typicality of measurements in the quantum Kac ring