Interestingly (to me!) it took a while in the 90’s/early 00’s for the community to realise that there are distinct questions:

Question A: Does there exist a set of target states and measurements that implement the task

Question B: Can mistrustful parties find a communication protocol that securely (from their perspective) create/implement those states/measurments.

An example where the answer to A is “no” is fully secure oblivious transfer. There were a bunch of misguided papers trying to find communication protocols for OT, but they were doomed from the start!

An example where the answer to A is “yes" but to B is “no” is strong coin flipping. And an example where the answer to both is “yes” is weak coin flipping. (See Carlos Mochon’s magnus opus arxiv 0711.4114 for the coin flipping examples).

I first articulated the distinction between A and B quant-ph/0202143 but left the proof about OT and Question A as an exercise to the reader! Roger Colbeck in arxiv 0708.2843 provided a simple proof and elucidated the whole situation a lot I think.

Give the humans an order 1,2,3,…, and let a referee read them in that order. Person k tosses one fair coin and reports H/T. The referee stops at the first time the reported heads exceed the reported tails. If N people were consulted, choose one of those N uniformly at random. Output heads iff that chosen person’s coin was heads.

For a one-pass version: instead of storing the whole consulted prefix, the referee can keep a single “currently marked” consulted person, and when the k-th consulted coin arrives, replace the mark by that new person with probability 1/k. When the process stops, the marked person is uniform among the consulted ones.

My first thought does not achieve the task: expand pi/4 as a sum of positive rational numbers, then have each human use a couple of fair coins from their own Bernoulli factory to output a coin that is heads with probability given by their assigned rational number. The n'th human gets told the partial sum up to that point, flips their bernoulli factory coin and either terminates the protocol if they get heads, otherwise they adds their term to the partial sum they received and passes it on. The problem is the information content in the partial sums will grow with n.

I have an extremely vague question; Is there one of these "stupid" ways of computing pi that doesn't involve an infeasible (to humans) infinity? I'm comparing to the "have pick people random integers and the probability they are coprime is 6/pi^2" method, which, again, to really work involves some poor people wasting an infinity of their lives. Your scheme does too from what I understand? Is this necessary?

Off topic: If you search for "quantum bernoulli factory" you will find some work I did that shows f(p)=2p is achievable if your "quantum coins" are presented as coherent superpositions instead of classical incoherent mixtures. Your work on exact sampling completely blew my mind (I'm a physicist!) while I was trying to undersantd that whole field.

If for any of these topics you do manage to get a summary you'd agree with from a (future or better-prompted?) LLM I'd like to read it. Particularly the first and third, the second is somewhat familiar and the fourth was a bit vague.

Is finding exponentially inefficient ways of factorizing interesting?

[And at least I knew his name already unlike our current laureates whom I just had to look up!]

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.10...

That particular proposal was mathematically wrong for reasons I still find physically perplexing (it turns out that for some events quantum theory allows for stronger memory records - defined via classial mutual information - of entropy decreasing events!). A simple example is in here: https://arxiv.org/abs/0909.1726 (I am second author).

Could anyone explain to me how they think this might work in practice?

I am presently producing an undergrad textbook in quantum theory. I have two motivations: 1. IMO the "qubits first" (ie teach finite-dimensional QM before wave mechanics) approach to introducing the theory is superior (basically only Feynman did it of all the "classic" books) and 2. I'm involved in third world education and I want the book to be freely downloadable.

Now its a lot of work despite having taught the course multiple times and produced comprehensive lecture notes etc. Once its done I am sure I will not have the time to keep updating it, expanding on the problem sets and so on. A former student on the course is helping with the conversion and he will be a co-author, but like me he sees it as a service not at all about producing a product. So I think we're both very open to the idea of such "open license".

Given all that here are the kinds of questions that immediately arise:

- Mechanically how should one make the book available for such re-working? Put the source files on github? (Not something I've ever used, but I know roughly how it works).

- Via what mechanism does someone get to be credited for work they might do on better versions?

- Who decides what is the current "definitive" or "best" version? I will have a separate website for the book so I guess new versions can be announced there. But one way or the other I won't be involved forever.

- QM is fraught with crackpots, people who have whacky ideas on how to explain things and so on. Can they be prevented from "taking over", rewriting large chunks into (what I would view as) nonsense and so on? Note that presumably my name would still be associated with the new versions, so the issue is primarily not lending credence to stuff I fundamentally disagree with, not that they shouldn't be allowed to go do their thing.

- We will make a POD service available for purchasing hardcopies, the (expected to be small) royalties from which would be donated to third world physics/math education. Is there some license that can ensure any subsequent use of the material is also similarly non-profit?

I can see some (though not perfect) analogies with open-source software, so perhaps someone here has useful ideas about this kind of thing already...

1. 1/2 (i.e fair - von Neumann)

2. p^2

3. p^2/(p^2+(1-p)^2)

4. sqrt(p)

Number 4 really surprised me, I learned it from this paper: http://www.math.chalmers.se/~wastlund/coinFlip.pdf

But you can never generate the biases:

5. 2p

6. 4p(1-p)

Although... if you change the game to allow a quantum coin then 5. and 6. are possible (a paper of mine: https://arxiv.org/abs/1509.06183)

The next step is not at all intuitive to me, namely that even someone trying to do a fair flip causes some precession, and that this isn't decoupled from the rotation.

https://ar5iv.labs.arxiv.org/html/2303.05514

The references come inline and not well separated from the text (eg in square brackets) like this:

Recently the world was introduced to PYTHEUS Ruiz-Gonzalez et al. (2022); Arlt, Ruiz-Gonzalez, and Krenn (2022). Like his homophonic namesake, PYTHEUS is an explorer, who in just a few short years has already made new scientific discoveriesArlt, Ruiz-Gonzalez, and Krenn (2022)!

I suspect this is related to me using bibtex poorly in the original or something!

Anyway, great work overall, thanks again :)

It seems to be using the bibtex tags for the inline citations. They don't stand out clearly enough for my liking, and they also have me worried: have I ever used a tag for someones paper like "XXXnonsense" or "dumbassYYY"?? Knowing myself, well....