The Quantum Butterfly Effect

https://discover.lanl.gov/publications/1663/2021-august/the-quantum-butterfly-effect/

by lr0 • 2 years ago

81 30 2 years ago

discover.lanl.gov

I'm used to articles like this having some citation, but this doesn't seem to have any. I know about los Alamos lab but not familiar with their writing, am I correct in assuming this is pre-published findings?

eigenket• 2 years ago

This is the relevant preprint

https://arxiv.org/abs/1903.02651

thecrims0nchin2• 2 years ago

Thank you. Embarrassed I missed this

refibrillator• 2 years ago

Paper (2020): 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• 2 years ago

I 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.

altruios2• 2 years ago

Boiling 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• 2 years ago

How does this interact with the 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?

hggh2• 2 years ago

(2021)

hggh2• 2 years ago

https://web.archive.org/web/20240819024055/https://discover....

oezi2• 2 years ago

“At the outset, it wasn’t clear that quantum chaos would even exist,” says Yan. “The equations of quantum physics give no immediate indication of it.”

Aren't the Copenhagen interpretation and Heisenberg uncertainty principle an immediate indication that Quantum systems can only be chaotic?

sieste2• 2 years ago

I think they are referring to the mathematical definition of "chaotic" (sensitivity to initial conditions, topological mixing, dense periodic orbits) which some equations and dynamical systems satisfy, but that was not immediately clear for the governing equations of QM.

oezi2• 2 years ago

From this mathematical definition, the dense periodic orbits seem very hard to be satisfiable in many natural systems which aren't bound by gravity or some other form of locality.

Vox_Leone• 2 years ago

>Aren't the Copenhagen interpretation and Heisenberg uncertainty principle an immediate indication that Quantum systems can only be chaotic?

Quantum systems are not chaotic but intrinsically indeterminate, insofar as the initial conditions of a system have no relation to the observed state. Chaotic systems are deterministic, and therefore classical. Quantum chaos tools attempt to bridge the gap.

https://en.wikipedia.org/wiki/Quantum_chaos

rbanffy2• 2 years ago

Interesting… feels like reality has an error-correction mechanism, that perturbations small enough can be smoothed out at a macroscopic scale.

dahart• 2 years ago

That seems unsurprising, right? Probably all physics we experience - light-surface interactions, surfaces at the atomic scale, and waves in air and water - are all made entirely of only small perturbations, but enough of them the result is statistically stable.

The popular idea of the butterfly effect in weather has always seemed suspect to me, due to the fact that air is a naturally damped system; a butterfly’s influence on air drops over distance, and likely falls off fast enough that the probability it can affect something even a few miles away is below atomic or quantum thresholds. The analogy between weather and simple mathematical chaotic systems seems specious.

Looking around a little it seems like some physicists are starting to agree, and believe Lorenz’ observations based on his weather modeling has more to do with the modeling and limited numerics than reality: “the limited predictability within the Lorenz 1969 model is explained by scale interactions in one article[22] and by system ill-conditioning in another more recent study.[25]” https://en.wikipedia.org/wiki/Butterfly_effect#Recent_debate...

phyalow• 2 years ago

I feel like its just getting at the main ideas of https://en.wikipedia.org/wiki/Statistical_mechanics (although I am technically lay in this field).

spiritplumber• 2 years ago

"Some days you're the simulation, some days you're the calamari." (If you know you know)

K0balt2• 2 years ago

This seems a bit self referential, if viewed from a many worlds interpretation.

The infinity of universes in which you can exist is reduced to a lesser infinity by the reverse time travel, since you could only have travelled backwards from universal states in which those specific conditions still existed, ergo reality appears to the traveller to be self healing.

That’s one of the things about MWI that is irritating, even though it still seems the most likely to me. It covers the testing parameters so completely that it is impossible to test. You always end up in a lesser infinity, but an infinity nonetheless. What we need is a way to quantify randomness in such a way that we might detect a change in the dimensions of infinities or something, but that seems improbable at best.

layer82• 2 years ago

The issue with Copenhagen is that it doesn’t describe when precisely wave-function collapse actually happens, i.e., when the physical process deviates from the Schrödinger equation. It is not a proper theory in that sense. There are objective-collapse theories that do, and therefore provide different predictions from Many-Worlds (which simply says that the Schrödinger equation always holds). We haven’t come up with experiments yet that could test those different predictions, but we may in the future.

rbanffy2• 2 years ago

I remember reading somewhere wave function collapse would have some energy signature and that someone failed to detect it, indicating the many worlds interpretation could not be ruled out.

nessus42• 2 years ago

Bohm's Interpretation is experimentally indistinguishable from MWI.

On the other hand, Bohm's interpretation seems pretty ad hoc. And it also includes all of the other worlds that MWI has in it via the pilot waves that continue to exist and propagate forever. (The pilot waves never collapse.) It's just that only one of those many worlds ends up being "real".

bigtimber• 2 years ago

https://phys.org/news/2020-07-simulating-quantum-butterfly-e...

ninju• 2 years ago

[2021]

mixtureoftakes• 2 years ago

it was just deleted? Page not found

stronglikedan• 2 years ago

nope. maybe hugged, but it's there now

The Quantum Butterfly Effect

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