If I'm reading the paper right, they're just doing a bad job of explaining measuring a qubit by phase kickback. And for some reason they're talking about batteries?
When they say "indefinite causal order" what they mean is they do this:
if C: do A
do B
if not C: do A
So C determines if A happens before or after B. Personally I would never describe that as "indefinite causal order". There's a very definite order. First you do "A if C" then you do "B" then you do "A if not C". Using fancy words to describe the effects of an `if` statement doesn't change that it's an `if` statement...
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.
I don't see the paper on arXiv (which is very very odd for a quantum mechanics paper), but PRL is usually legit. I don't seem to get to read PRL papers for free, though :(.
In an effort to figure out what the authors are talking about, I found this earlier paper:
> 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.)
Note: I was basing my comments on the arXiv preprint https://arxiv.org/abs/2105.12466 "Indefinite Causal Order in Quantum Batteries", which I assumed was the preprint for the PRL paper. It's conceivable that it's not... certainly substantial rewrites have occurred (the title and abstract have changed, and there's an additional author, though the gist looks the same).
> When they say "indefinite causal order" what they mean is they do this:
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
When they say "indefinite causal order" what they mean is they do this:
So C determines if A happens before or after B. Personally I would never describe that as "indefinite causal order". There's a very definite order. First you do "A if C" then you do "B" then you do "A if not C". Using fancy words to describe the effects of an `if` statement doesn't change that it's an `if` statement...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