3 ms·
Paper (2020): https://arxiv.org/pdf/2003.07267 https://arxiv.org/pdf/2003.07267 As a layperson I found the first page to be more succinct and intuitive than th
by refibrillator 2y ago
Paper (2020): https://arxiv.org/pdf/2003.07267 https://arxiv.org/pdf/2003.07267
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.
- whatshisface 2y agoI don't get how the no-hiding theorem implies that the information will be preserved in the remaining qbits, if the "environment" of the measurement is the lab, not the available ancilla.
- altruios 2y agoBoiling this down further... f(cQbit)=> bath = decompose(cQbit) Bath now has information about the central Qbit stored in the bath. Any measurement of cQbit changes the state of cQbit and destroys any correlation with the bath. Regardless of the state of cQbit: you can rebuild the cQbit with the information about cQbit stored in the bath. f(bath)=> cQbit = compose(bath) This effect seems trivial as I've explained it. So I assume I got something wrong. Is it just the process of restoring from the bath into the cQbit that's complicated, or has a bunch of gotcha's? It seems like the state of the cQbit is inconsequential if you can just overwrite (:ah... the gotcha) it with the info from the bath.
- martincmartin 2y agoHow does this interact with the No Cloning Theorem? https://en.wikipedia.org/wiki/No-cloning_theorem https://en.wikipedia.org/wiki/No-cloning_theorem If you can rebuild the cQbit from just the bath, then there's no information in cQbit, right?
- altruios 2y agoI'm a layman here: so much salt to take with this. I assume the factors that mitigate/negate the no-cloning theorem are that the bath is not a qBit, but a collection, that the state's are initially entangled. It could also be that the initial state of the cQbit is known, instead of unknown. the no-broadcast-theorem is what covers mixed states instead of pure states. https://en.wikipedia.org/wiki/No-broadcasting_theorem https://en.wikipedia.org/wiki/No-broadcasting_theorem ``` The theorem[1] also includes a converse: if two quantum states do commute, there is a method for broadcasting them: they must have a common basis of eigenstates diagonalizing them simultaneously, and the map that clones every state of this basis is a legitimate quantum operation, requiring only physical resources independent of the input state to implement—a completely positive map. A corollary is that there is a physical process capable of broadcasting every state in some set of quantum states if, and only if, every pair of states in the set commutes. This broadcasting map, which works in the commuting case, produces an overall state in which the two copies are perfectly correlated in their eigenbasis. ``` So it seems that there is some wiggle room, and specifically when you start working with collections instead of single qbits, things get weird. But I'm a layman, and that was just a walk down wikipedia.
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