The no-hiding theorem[1] states that if information is lost from a system via decoherence, then it moves to the subspace of the environment and it cannot remain in the correlation between the system and the environment. This is a fundamental consequence of the linearity and unitarity of quantum mechanics. Thus, information is never lost. This has implications in the black hole information paradox and in fact any process that tends to lose information completely. The no-hiding theorem is robust to imperfection in the physical process that seemingly destroys the original information.
This was proved by Samuel L. Braunstein and Arun K. Pati in 2007. In 2011, the no-hiding theorem was experimentally tested[2] using nuclear magnetic resonance devices where a single qubit undergoes complete randomization; i.e., a pure state transforms to a random mixed state. Subsequently, the lost information has been recovered from the ancilla qubits using suitable local unitary transformation only in the environment Hilbert space in accordance with the no-hiding theorem. This experiment for the first time demonstrated the conservation of quantum information.[3]