Talk:Quantum pseudo-telepathy

The rules of play are not explained well

From the description in the article, it's almost impossible to figure out either the "rules of game play", or the "algorithm" that Alice and Bob employ. The reason is that it is not presented in a step-by-step, cookbook kind of way, but rather it is kind of "induced" by already knowing what to expect in these kinds of problems.

Here are some of the missing steps.

(1) Is each round of the game a separate game, or do they accumulate?

Separate game. But you repeat the game over and over as often as you like and try to win as often as possible. Using the quantum method described, Alice and Bob can win all the time.

(2) Do they have to fill in the whole board? Do they get to see the board between rounds? How do they fill in the rest of the board without conflicts?

Each round is a separate game. They don't fill in the whole board, only one row and column (5 squares). The square of intersection gets two values. If the two values agree, they win. If the two values disagree, they lose. That is the whole game.

After the game, Bob and Alice learn the results, or they don't -- not important. The board is then cleared for the next round.

(3) How do you win?

They win or lose together, because it is a cooperative game. They win if they agree on the square of intersection. They lose if they disagree. But they are constrained by the parity rules described in the article.

(4) How are the rows and columns selected?

Either randomly or by an enemy, who tries to make life hard for A & B by affording no predictability.

(5) How do they implement their strategy?

Their algorithm is as follows.

First, they have a shared "secret", the tangled state |φ> consisting of 4 particles. Alice can make measurements on particles a and c. Bob can make measurements on particles b and d.

They plan to use the spin measurement operators S_x ⊗ I, etc, listed in the 3x3 table to create their moves. This is their "reading device" for the secret.

The "secret" together with the "reading device" is their "table". It is better than a deterministic table because it allows quasi-telepathy.

When Alice learns which row she has to fill in, she uses that information to select which observations she makes on |φ>. She needs 3 observations since she has to put 3 numbers in the selected row. She uses the 3 operators in the selected row to make her measurements. But she only has access to the particle in the first and third factors (particles a and c) of the tensor product, so she uses the operators on these.

(Here I don't know quite what operators to insert where, nor why she is allowed to do 3 measurements instead of just one.)

((The operators to be used are the operators indicated in each box. You need one measurement per box. There are three boxes in each row, thus 3 measurements))

She uses each of the 3 operators to read the value of an observable from |φ>. She gets 3 numbers, which she puts in her row.

Bob does something similar for his column.

Where the row and column intersect, a full measurement has been done. The structure of |φ> and of the 3x3 operator chart is such that the outcomes in the intersection square correlate perfectly with each other (they are always equal). But their equal value is random.

The outcome in the other four squares is also fairly random. But there are some regularities, because of the structure of the 3x3 operator chart. Namely, the product of the rows is always even. The product of the columns is always odd.

Another important thing is true. Namely, there is no communication between Alice and Bob outside of their remarkable ability to consistently win the game. They can't use the measurement process to communicate even one extra bit of information (provided by the enemy) with any degree of reliability above pure random chance -- not even if they are allowed to forget about winning and decide by themselves which measurements to make. This is called "non-communication" and is a very general result about any entangled quantum state with two separated observers. It is true for joint conditional probabilities that emerge from a quantum calculation, but not necessarily for even more general choices of joint, conditional probabilities. Non-communication is expressed by a statement about independence of certain joint conditional probabilities (conditional upon what measurement is chosen), without reference to the way they are derived. But this is another story and treated elsewhere.

89.217.12.73 (talk) 23:05, 29 April 2015 (UTC)

Okay, I edited the page to improve the presentation of the rules of game play (items (1)-(4) above).

But I still am puzzled about (5). Maybe the key is to use the identity matrix I for the missing factors in the tensor product -- to get a partial trace which becomes a mixed state for Alice or Bob?? But I still don't see why they're allowed to make 3 measurements, or if this is needed. (2 seems okay since there are 2 particles each.)

In summary: How do Alice and Bob determine from the 3x3 operator chart how many and which measurements to perform, and where on |φ> do they place which operators to perform them?

89.217.12.73 (talk) 23:57, 29 April 2015 (UTC)

One makes one measurement per box, always. One measures only one entangled state per round of play. One can make three measurements on it, as long as all three measurements are of operators that commute. The rows and columns are set up so that the opers commute in each row, and in each column. The middle row/column may seem confusing, but if you look at it carefully, you will see that the operators commute there, as well. That is, although sigma-x does NOT commute with sigma-y, the product sigma-x otimes sigma-x DOES commute with the product sigma-y otimes sigma-y, thus it is possible to measure both of these on one single state. Note that *all four* particles are entangled, and not just two pairs. 67.198.37.16 (talk) 17:20, 2 November 2016 (UTC)

sign of middle entry in magic square

Multiplying all entries in a row or column I get -1 for the middle row and +1 for the middle column. That differs from the statement made in the paragraph above it (all rows multipying to +1, all columns multiplying to -1). Has the middle entry the wrong sign?

The magic square in the article also differs from the one in the quoted document "P. K. Aravind". That one has 3 rows and 2 columns multiplying to +1 and one column multiplying to -1. What is the reason for this difference? — Preceding unsigned comment added by 159.100.91.136 (talk) 20:19, 27 December 2016 (UTC)

Blatant falsehood

‘Note that all four particles are entangled: the above is a single state, and not two distinct, separable Bell states.’ That's what the article says. But the state is (|00>+|11>)x(|00>+|11>). How is this not separable? — Preceding unsigned comment added by 67.221.69.72 (talk) 23:46, 2 March 2018 (UTC)

Yeah I think it should be a pair of entangled pairs rather than 4 entangled qubits (Jeremiah Vocaturo (talk) 22:12, 14 March 2019 (UTC))

This article is confused.

Most of this article is about the Mermin-Peres magic squares game. This concept was developed to help explain Bell's theorem. It has a history all its own.

Then in 2005 a paper established a connection to another theory:

• "Recasting Mermin's multi-player game into the framework of pseudo-telepathy" Gilles Brassard, Anne Broadbent, Alain Tapp

So the result here is an article about magic squares hiding in an article about another topic. Johnjbarton (talk) 02:24, 27 March 2024 (UTC)

Also there are articles, eg

• Device-Independent Quantum Key Distribution Based on the Mermin-Peres Magic Square Game

Yi-Zheng Zhen, Yingqiu Mao, Yu-Zhe Zhang, Feihu Xu, and Barry C. Sanders

Phys. Rev. Lett. 131, 080801 – Published 25 August 2023

which discuss Mermin-Peres game without discussing pseudo-telepathy.

I generally argue to delete or merge articles, but here I wonder if the better solution is to split. Johnjbarton (talk) 18:04, 27 March 2024 (UTC)

It's true that the Peres-Mermin square is in principle independent, and probably notable on its own, but I don't see the benefit in splitting. I removed a lot of dubious material from the article, I think now it's much better focused. Without the Peres-Mermin square there won't be much left. Tercer (talk) 19:51, 27 March 2024 (UTC)

@Tercer what do you think about renaming it? I think it would be a better article as Mermin-Peres magic square with a section relating it to pseudo-telepathy. Johnjbarton (talk) 20:42, 27 March 2024 (UTC)

I don't think that's a good idea. There are plenty of incoming links, and I think we should have an article about quantum pseudo-telepathy. It's clearly not in a good state, but I think it should be improved rather than eliminated. Tercer (talk) 21:11, 27 March 2024 (UTC)

A lot of those incoming links are from items thrown into "See also" sections, which don't really make the case that quantum pseudo-telepathy is the primary topic ("see also" sections in this corner of the project tend to accumulate whatever somebody thought sounded cool). A few others link to the Mermin–Peres magic square section, like the biography pages for Mermin and Peres themselves. A crude GS search finds 600-ish results excluding "telepathy" versus only 83 including it — a very rough measure, to be sure, but consistent with my overall feeling that the Mermin–Peres magic square can stand on its own as an article topic, while quantum pseudo-telepathy is one way it can be thought about. Perhaps we can cover quantum pseudo-telepathy in quantum game theory and have an article about the magic square specifically.

I don't have strong feelings about any of this, and I'm sure that many different organizational schemes would all be justifiable. The current arrangement just seems a little odd. XOR'easter (talk) 22:39, 27 March 2024 (UTC)