[HN Gopher] The Quantum Butterfly Effect
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The Quantum Butterfly Effect
Author : lr0
Score : 73 points
Date : 2024-08-15 05:46 UTC (4 days ago)
(HTM) web link (discover.lanl.gov)
(TXT) w3m dump (discover.lanl.gov)
| thecrims0nchin wrote:
| 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 wrote:
| This is the relevant preprint
|
| https://arxiv.org/abs/1903.02651
| refibrillator wrote:
| 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 wrote:
| 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_.
| altruios wrote:
| 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 wrote:
| 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?
| altruios wrote:
| I'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
|
| ``` 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.
| hggh wrote:
| (2021)
| hggh wrote:
| https://web.archive.org/web/20240819024055/https://discover....
| oezi wrote:
| > "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?
| sieste wrote:
| 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.
| oezi wrote:
| 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.
| sieste wrote:
| the definition refers to periodic orbits in phase space.
| Vox_Leone wrote:
| >>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
| rbanffy wrote:
| Interesting... feels like reality has an error-correction
| mechanism, that perturbations small enough can be smoothed out at
| a macroscopic scale.
| dahart wrote:
| 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 wrote:
| 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 wrote:
| "Some days you're the simulation, some days you're the calamari."
| (If you know you know)
| K0balt wrote:
| 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.
| layer8 wrote:
| 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 Schrodinger 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
| Schrodinger equation always holds). We haven't come up with
| experiments yet that could test those different predictions,
| but we may in the future.
| rbanffy wrote:
| 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.
| Enginerrrd wrote:
| The only thing I can think of that you might be thinking of
| is that as far as I know, MWI really requires QM be
| perfectly linear.
|
| I'm not 100% sure, but wave function collapse might involve
| some non-linearity somewhere, whichight also be detectable
| in some fashion.
| nessus42 wrote:
| 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".
| layer8 wrote:
| Yes, Bohmian mechanics seems like MW with added
| complications, all the "worlds" still exist. It's not clear
| how it is ontologically different from MW, other than that
| painting one of the worldlines green.
| bigtimber wrote:
| https://phys.org/news/2020-07-simulating-quantum-butterfly-e...
| ninju wrote:
| [2021]
| mixtureoftakes wrote:
| it was just deleted? Page not found
| stronglikedan wrote:
| nope. maybe hugged, but it's there now
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