Paper (2020):
https://arxiv.org/pdf/2003.07267As a layperson I found the first page to be more succinct and intuitive than the article.
> Let Alice have such a processor that implements fast information scrambling during a reversible unitary evolution of many interacting qubits. She applies this evolution to hide an original state of one of her qubits, which we call the central qubit. The other qubits are called the bath. To recover the initial central qubit state, Alice can apply a time-reversed protocol.
> Let Bob be an intruder who can measure the state of the central qubit in any basis unknown to Alice. If her processor has already scrambled the information, Alice is sure that Bob cannot get anything useful. However, Bob’s measurement changes the state of the central qubit and also destroys all quantum correlations between this qubit and the rest of the system.
> According to the no-hiding theorem, information of the central qubit is completely transferred to the bath during the scrambling process. However, Alice does not have knowledge of the bath state at any time. How can she recover the useful information in this case?
> In this Letter, we show that even after Bob’s measurement, Alice can recover her information by applying the time-reversed protocol and performing a quantum state tomography with a limited amount of effort. Moreover, reconstruction of the original qubit will not be influenced by Bob’s choice of the measurement axis and the initial state of the bath.
> This effect cannot be explained with semiclassical intuition. Indeed, classical chaotic evolution magnifies any state damage exponentially quickly, which is known as the butterfly effect. The quantum evolution, however, is linear. This explains why, in our case, the uncontrolled damage to the state is not magnified by the subsequent complex evolution.
As a layperson I found the first page to be more succinct and intuitive than the article.
> Let Alice have such a processor that implements fast information scrambling during a reversible unitary evolution of many interacting qubits. She applies this evolution to hide an original state of one of her qubits, which we call the central qubit. The other qubits are called the bath. To recover the initial central qubit state, Alice can apply a time-reversed protocol.
> Let Bob be an intruder who can measure the state of the central qubit in any basis unknown to Alice. If her processor has already scrambled the information, Alice is sure that Bob cannot get anything useful. However, Bob’s measurement changes the state of the central qubit and also destroys all quantum correlations between this qubit and the rest of the system.
> According to the no-hiding theorem, information of the central qubit is completely transferred to the bath during the scrambling process. However, Alice does not have knowledge of the bath state at any time. How can she recover the useful information in this case?
> In this Letter, we show that even after Bob’s measurement, Alice can recover her information by applying the time-reversed protocol and performing a quantum state tomography with a limited amount of effort. Moreover, reconstruction of the original qubit will not be influenced by Bob’s choice of the measurement axis and the initial state of the bath.
> This effect cannot be explained with semiclassical intuition. Indeed, classical chaotic evolution magnifies any state damage exponentially quickly, which is known as the butterfly effect. The quantum evolution, however, is linear. This explains why, in our case, the uncontrolled damage to the state is not magnified by the subsequent complex evolution.