When they say "indefinite causal order" what they mean is they do this:

    if C: do A
    do B
    if not C: do A

A key thing to understand here is kickback[1][2]. Something you get used to very quickly when learning quantum computing is that anytime you see "if C: do A" you need to understand how this might change C. The underlying issue is that in quantum mechanics all interactions are two way streets. For an "if" statement you want the condition to determine the action, without the action affecting the condition. But your building blocks fundamentally don't allow this. So any actual implementation of "if C: do A" will have what's called kickback, where an operation is applied to C depending on A.

Anyways, they do this series of instructions where C appears as a condition. Then they measure C. Due to kickback, this is revealing information about the state of the battery. Sometimes it collapses to being charged. That's the paper.

1: https://en.wikipedia.org/wiki/Quantum_phase_estimation_algor...

2: https://www.youtube.com/watch?v=EjdngeGXWEg&t=100

In an effort to figure out what the authors are talking about, I found this earlier paper:

https://arxiv.org/pdf/2112.03233.pdf

I'll mostly ignore goodies like this:

> In simple words, non-determinism of the quantum theory and the dynamical causal structure in general relativity may give rise to novel causal structures. What this implies is that one may expect the existence of processes whose causal order becomes indefinite in a theory of quantum gravity, the main goal of which is to reconcile the two above-mentioned solid pillars of modern physics

What does this have to do with quantum gravity? Quantum mechanics plus special relativity (which don't have any of the hairy issues associated with quantum gravity) gives spacelike-separated events, which don't have a definite causal order.

Anyway, the paper seems to be trying to say that one can take two qubits, operate on them locally (i.e. do quantum operations individually on each one but no joint quantum operations between them and anything else) and end up with them being entangled. Off the top of my head (haven't tried to prove it, but I suspect I could prove it very easily under reasonable assumptions), this is impossible.

But the paper gets around it using a "quantum switch". This is just a plain old controlled operation with a control qubit, and it's laid out in its full generality in equation (1), which can be summarized as:

[the operation being performed] = |0><0|_C ⊗ (operation on "target 1") + |1><1|_C_ ⊗ (operation on "target 2")

(I've elided a whole bunch of Kraus operators, and I'm not especially happy about how they wrote it without clearly identifying which system each piece of this process acts on. Something like |0><0| ⊗ A ⊗ I + |1><1| ⊗ I ⊗ B would have been nicer, and the use of CPTP maps seems more general than needed -- plain old unitary matrices on the state vectors would be just fine.)

THIS IS NOT A LOCAL OPERATION ON EACH TARGET! Even just looking at the expression, it does not decompose like X ⊗ Y ⊗ Z!

"Local" means you don't do quantum stuff that extends outside the thing in question. This is a very much non-local process. You can write it like this (in which case it's a mildly restricted class of operations on three systems), or you can try to write it as a sequence of two operations, one on the control and target 1 and one on the control and target 2, in which case they had better commute if you want to continue to believe that causal order is irrelevant.

But saying that you, locally, without a definite causal order, did both of these things at once, seems like a HUGE stretch. You can certainly do two things in indefinite order, and it looks like:

[the result] = [what you do to target 1] ⊗ [what you do to target 2]

That is not the same thing, sorry. If the order is really indefinite, then you are not allowed to set up an experiment in which you could potentially measure the order, and if you throw in a magic switch that selects the order, you can measure which order they're in (assuming you pick operations that allow this).

So, no, I don't think that any local, causally disconnected things are making EPR pairs.

And I'm highly unconvinced that lasers beams right next to each other, with what are presumably entangled beams, are magically charging a battery better than expected. I would at least hope to have a very clear explanation of what the claim means.

(Source: I have a PhD in this stuff. And I tried to make a point of very clearly defining what I was talking about in my papers.)

That reminds me of a funny presentation which is basically "if we engineered a bunch of exotic sci-fi concepts... what would the perl programs running on them look like?"

More formally: "Temporally Quaquaversal Virtual Nanomachine Programming In Multiple Topologically Connected Quantum-Relativistic Parallel Timespaces... Made Easy!" - https://www.youtube.com/watch?v=ORjyXcLDd9M

“Breaks the intuitive notion of causality”, maybe.

> In the classical world, if you tried to charge a battery using two chargers, you would have to do so in sequence, limiting the available options to just two possible orders.

Uhhhh. Of course you can charge in parallel, just like you can power something from batteries in parallel. How do they think a solar panel array charges a battery at a specific voltage while increasing wattage of the array? -- parallel solar panels => parallel charging.

I don't know if it's a translation peculiarity or what, but the whole thing seems off.

> Earlier methods to charge a quantum battery involved a series of charging stages one after the other. However, here, the team instead used a novel quantum effect they call indefinite causal order, or ICO. In the classical realm, causality follows a clear path, meaning that if event A leads to event B, then the possibility of B causing A is excluded.

I don't blame the authors for interpreting this as causality being broken, as most programmers know how difficult causality is to think about once you have concurrent processes in play.

My guess is:

The "battery" is an atom that can be in the ground state or exited.

The two chargers are laser, let's call them A and B

A classic "battery" can go:

* Empty (total = 0) -> absorb a photon from A (total = A) -> absorb a photon from B (total = A+B)

or

* Empty (total = 0) -> absorb a photon from B (total = B) -> absorb a photon from A (total = A+B

But a quantum "battery" can go:

* Empty (total = 0) -> 50% absorb a photon from A and 50% absorb a photon from B and (total = (A+B)/2) -> absorb the other photon (total = A+B)

where 50%+50% is actually 1/sqrt(2)±1/sqrt(2) for technical reasons. (They are not absorbing the 50% of the photon.)

I don't understand the part of the weaker charger. If the laser A and B have the same frequency/color, then it does not make sense. If they are different, it is almost obvious because fine tuning the energy of the photons in the laser to the energy of the transitions of the levels of an atom is a good idea to promote absorption.

As I said, I'm guessing too much, so I'd be happy if anyone can post a better explanation.

It looks like a previous work. It looks like it's a single qubit going from 0 to 1.

Charger 1 is connected using the Pauli matrix σx and Charger 2 is connected using the Pauli matrix σy. σx and σy does not conmute, so using the chargers in different order get a different result.

From the preprint:

> A quantum switch that realizes indefinite causal order admits higher-order processes where a control qubit plays the role of determining the order of occurrence of C1 and C2. Depending on the control qubit’s initial state, infinitely many configurations become possible, e.g., when the control qubit is prepared in a coherently balanced state, the battery undergoes the charging dynamics determined by C1C2 and C2C1 in a balanced superposition. A measurement will be performed on the control qubit following the dynamical evolutions of the target system.

It looks like standard superposition with strange names.

IIUC they make measurements and repeat the operation, and that increase the probability that the final state of the qubit is 1. This second part may be interesting, but the unusual names make me decide to forget it.

One cannot assume the charge will be split 50/50 because its probabilistic and how the atoms are impacted by the photos may impact charge. Also, it may be the case that - probabilistically - the charge is no better or more efficient than a classic battery. Anyway, I think this explains how a lesser charge may result in a higher stored charge.

Yes, that's true. One of the confusing things is that this "indefinite causal order" thing is very limited--for example, you can't use it to send actual information faster than light. It can produce correlations that seem to defy our usual intuitions about cause and effect, but to actually make use of such things, you have to wait for ordinary classical (i.e., light speed or slower) transmission of the information you need to do so.

For example, in the Alice an Bob scenario at the start of the Quanta magazine article you linked to, while it's possible for Alice's dropping the plate and Bob burning himself to be correlated in ways that defy our classical intuitions, Alice can't make any use of the fact that Bob burned himself until the information from Bob reaches her at light speed or slower, and Bob can't make any use of the fact that Alice dropped the plate until the information reaches him at light speed or slower.

(Btw, the article is misleading on this point, since it describes Alice as dropping the plate when she hears Bob cry out in one version, and Bob burning himself when he hears Alice drop the plate in the other version. If the Alice and Bob events are spacelike separated, which is the scenario that causes all the head scratching, these descriptions are wrong--Alice and Bob can't hear each other faster than light. A proper description would be something like: Alice drops a plate for no apparent reason, she says it just happened out of the blue before she could react; and Bob burns himself for no apparent reason, he says it just happened out of the blue before he could react; but it turns out that every time these things happen, they happen together--Alice never drops a plate without Bob burning himself, and vice versa.)

So it's even possible to interpret all this as not changing our concept of "causality" at all, just putting a little quantum wrinkle in that only has limited effects.

Not just due to quantum effects; due to the fact that the time ordering of the events is not invariant; it's different in different frames. The quantum effects come in because without them the correlations would not be there and there would be nothing counterintuitive to explain.

> there are multiple causal orderings

In the sense that the time ordering of the events is not invariant, yes, you can say that. But relativity says that no actual physics can depend on something that's not invariant and depends on your choice of reference frame, so really it would be better to say that there is no ordering; the ordering is undefined and can't play a role in anything.

> and they are all valid due to superposition

No, superposition does not play a role here. We're talking about measurement results; there is no superposition of those. For example, Alice drops the plate and Bob burns himself. There's no superposition there, just two results that always occur together, and classical physics can't explain why. Quantum mechanics can, and its explanation implies that there is some connection between the two events, but if it's a causal connection, it must be one that can "work" in either order, so to speak--or more precisely, that doesn't have to "know" anything about ordering to work.

Unfortunately no real causality is actually broken.

Hard to me more un-understandable than that.

Well, they're no use if they run out before you even use them! Maybe causality operates at a different voltage?

If they have something that isn't nonsense, they can write a better article.

"Don't you even DARE look at at the power guage! The moment you do, the observation will collapse the battery state superposition, stranding us in the middle of Nevada!"

Announcer: "And it's a dead heat! They're checking the electron microscope ... and the winner is, number 3, in a quantum finish!"

Professor: "No fair! You changed the outcome by measuring it!"