No, quantum information generally does not remain coherent after decoherence. Decoherence refers to the loss of quantum coherence and the transition of a quantum system to a classical-like state due to its interaction with the surrounding environment.
When a quantum system interacts with its environment, it becomes entangled with the environmental degrees of freedom. These interactions cause the quantum superposition and entanglement of the system to become fragile, leading to the loss of coherence. The environment effectively acts as a measuring apparatus, causing the collapse of the quantum state into a classical-like mixture of states.
Once decoherence occurs, the quantum information encoded in the system becomes difficult to recover. The system loses its ability to exhibit quantum effects such as interference and entanglement, and the information it carries becomes spread out and entangled with the environment, making it challenging to extract useful quantum information.
However, it's worth noting that decoherence is a gradual process, and the timescale over which coherence is preserved can vary depending on the specific system and its interaction with the environment. In some cases, techniques such as quantum error correction can be employed to mitigate the effects of decoherence and preserve quantum information for longer periods.