The fourth lesson focused on chapters 6 and 7 of the lecture. When the environment acts collectively on the qubits, it is possible to encode information in so-called subradiant subspaces, preparing states protected by decoherence interference processes. A simple example of subradiant states can still be found in cavity electrodynamics. These are superpositions of tensor products of N two-level atoms unable to radiate into a cavity to which they are symmetrically coupled. These states belong to a subspace of the global space of N atoms. The information can thus be protected from decoherence due to radiation from the atoms in the cavity, provided it is encoded in this subspace. Starting with N independent atoms, all we need to do is add a further q qubits to create a subradiant subspace of the N + q qubit set as large as the initial space. Adding these few qubits and encoding the information in the subradiant set is known as "noise-free coding". The number of additional qubits required to achieve this noise-free coding is small, which may appear surprising but is merely an obvious property of the exponential law. Despite its theoretical interest, the noise-free coding method has limited practical scope. Situations in which noise acts completely symmetrically on the qubits are highly specific (e.g. radiation from identical atoms in a cavity) and difficult to implement. In the general case, the environment acts more or less independently on the qubits, and its effects cannot be corrected by this type of method.
The second part of the fourth lesson focused on the Zeno effect, sometimes described as an effective solution for protecting a system from decoherence. The Zeno effect has often been presented as a paradoxical quantum phenomenon (" watching a system prevents it from evolving") . The effect is less surprising than it might seem, if we note that observing a quantum system necessarily disturbs it. A rapidly repeated observation, as well as a continuous measurement, corresponds to a significant perturbation, with entanglement of the system's states with the states of the measuring apparatus. Perturbation theory then implies that the system's free Hamiltonian cannot effectively couple together eigenstates that differ from this perturbation. When the system interacts with a large environment, inhibition of evolution requires that the perturbation acts during the generally very short correlation time of the process. This condition makes the effect unobservable, except in a few special cases where the correlation time is relatively long. The Zénon effect is generally associated with a measurement, but its characteristics can be found for any rapid perturbation of the system, even if it is not an explicit measurement. In particular, the rapid periodic change in the sign of a system's interaction with its environment can slow down the decoherence of a system, with the effect showing analogies with the spin echo method. Like noise-free coding , this is still a special method of decoherence control that cannot be applied generally.
