Quantum Darwinism in a Composite System: Objectivity versus Classicality

We investigate the implications of quantum Darwinism in a composite system with interacting constituents exhibiting decoherence-free subspace. consider two-qubit coupled to an $N$-qubit environment via dephasing interaction. For excitation preserving interactions between qubits, analytical expression for dynamics is obtained. It demonstrates that part Hilbert space redundantly proliferates its information environment, while remaining subspace decoupled and preserves clear non-classical signatures. measurements performed on system, we establish non-zero discord shared thus violating conditions strong Darwinism. However, due asymmetry discord, completely classical environment. Our results imply dichotomy objectivity classicality emerges when considering systems.