We revisit decoherence process of a qubit register interacting with a thermal bosonic bath. We generalize the previous studies by considering not only the registers behavior but also of a part of its environment. In particular, we are interested in information flow from the register to the environment, which we describe using recently introduced multipartite quantum state structures called Spectrum Broadcast Structures. Working in two specific cases of: i) two-qubit register and ii) collective decoherence, we identify the regimes where the environment acquires almost complete information about the register state. We also study in more detail the interesting causal aspects, related to the finite propagation time of the field disturbances between the qubits. Finally, we describe quantum state structures which appear due to the presence of protected spaces.
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