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Scrambling prevents the access to local information with local operators andtherefore can be used to protect quantum information from damage caused bylocal perturbations. Even though partial quantum information can be recoveredif the type of the damage is known, the initial target state cannot becompletely recovered, because the obtained state is a mixture of the initialstate and a maximally mixed state. Here, we demonstrate an improved scheme torecover damaged quantum information via scrambling in indefinite casual order.We can record the type of damage and improve the fidelity of the recoveredquantum state with respect to the original one. Moreover, by iterating theschemes, the initial quantum state can be completely retrieved. In addition, weexperimentally demonstrate our schemes on the cloud-based quantum computer,named as Quafu. Our work proposes a feasible scheme to protect whole quantuminformation from damage, which is also compatible with other techniques such asquantum error corrections and entanglement purification protocols.

Recovery of damaged information via scrambling in indefinite casual order