Recovery of damaged information via scrambling in indefinite casual order

Abstract: Scrambling prevents the access to local information with local operators and therefore can be used to protect quantum information from damage caused by local perturbations. Even though partial quantum information can be recovered if the type of the damage is known, the initial target state cannot be completely recovered, because the obtained state is a mixture of the initial state and a maximally mixed state. Here, we demonstrate an improved scheme to recover damaged quantum information via scrambling in indefinite causal order. We show that scheme with indefinite causal order can record information of the damage and distill the initial state from the damaged state simultaneously. It allows us to retrieve initial information versus any damage. Moreover, by iterating the schemes, the initial quantum state can be completely recovered. In addition, we experimentally demonstrate our schemes on the cloud-based quantum computer, named as Quafu. Our work proposes a feasible scheme to protect whole quantum information from damage, which is also compatible with other techniques such as quantum error corrections and entanglement purification protocols. We expect that our scheme will be useful in the both quantum information recovery from the damage and systems bench-marking.