Quantum ‘Telepathy’: Mermin-Peres Magic Square (MPMS)

September 2023

By: Erica Low Sin Mun

“Telepathy could be advantageous for winning at bridge, a card game where partners must subtly communicate the strength of their hands to each other.”

Let’s delve into quantum “telepathy”! Crazy it may seem but … physicists suspected that if bridges were played using cards governed by the rules of quantum mechanics, something that looks uncannily like telepathy should be possible. Researchers in China conducted an experiment, which is a competition called the Mermin-Peres magic square (MPMS) game, demonstrating quantum pseudotelepathy. where winning requires that the players coordinate their actions without exchanging information with each other. Using laser photons, they achieved a flawless performance, pushing quantum mechanics' boundaries in information sharing between particles. This concept was initially formulated in 1990 by quantum physicists Asher Peres and David Mermin.

Classical MPMS Game

Alice and Bob, typical names used in this quantum scenario, where they must fill a 3x3 grid with +1 or -1 values. A referee, Charlie, assigns a random row to Alice and column to Bob, and they must determine the values for their respective grid spots. Winning requires both to select the same value where the row and column intersect. In classical scenarios, winning all rounds is impossible due to the classical conflict, where a person needs a +1 and the other needs a -1. However, they can achieve eight out of nine wins at best.

Quantum MPMS Game

They assign it a pair of quantum bits (qubits), each of which has a value of +1 or −1 when measured. The value given by each player to a particular grid element is determined by measuring the two qubit values and finding the product of the pair. Now the classical conflict can be avoided because both of them can obtain different values from the same two qubits depending on how they make their measurements. There is a particular measurement strategy that will ensure the winning criteria for any given round—that the products of Alice's and Bob's three entries are +1 and −1, respectively—are met for all 9 permutations of rows and columns. However, to ensure making the right set of measurements, Alice and Bob need to know which of their 3 grid elements is the one that overlaps with the other players. In other words, coordination is essential. But in the MPMS, they can do so easily because they take measurements one after the other on the same 3 pairs of qubits. When the measurement results get to Bob, he can tell from them how Alice measured her qubits. This way, they can share information with each other and figure out which grid element they're both observing.

CONTEXTUALITY

In 1993, Mermin demonstrated MPMS could illustrate contextuality, a quantum phenomenon that refers to the fact that the outcome of a quantum measurement may depend on how the measurement is done. Unlike classical measurements, quantum measurement doesn’t always give the same results. In the MPMS, the contextuality arises from the fact that the measurement for a given qubit pair may give a different result depending on which other two pairs are being measured.

QUANTUM PSEUDOTELEPATHY

But what if we forbid any communication in the MPMS? In a 2005 study, quantum theorist Gilles Brassard and his colleagues showed that the players can use quantum principles to guarantee a win in every round even without communicating by using what they called “quantum pseudotelepathy”. This strategy involves entangling one qubit from each of the pairs sent to Alice or Bob with a corresponding qubit used by the other player. Entangled particles have correlated properties. If Alice measures her qubit, the value of Bob's qubit becomes definite too, even though we can't predict the specific value of Alice's qubit before she measures it. They could be opposite, like +1 and -1. This linked property between the qubits is called "nonlocal”. In other words, it's shared between them and isn't tied to just one. Even if the qubits are far apart, they still act as a single connected unit. Adán Cabello proposed this idea in a 2001 game, and it's similar to the strategy in the MPMS experiment.

SHARED ENTANGLEMENT

Imagine, Alice and Bob have a magical way of sharing information without any interaction. How so? They each have qubit pairs that are connected in a mysterious way called "entanglement." In simpler terms, despite the vast distance, both particles are correlated and can affect one another. The cool thing is that they don't need to exchange any messages to coordinate their actions because the particles are already connected. With that being said, they’re able to outsmart normal rules and use these particles to solve problems faster than regular computers. This is really useful in "quantum computing."

Experiments were conducted with these magical qubits, using photons, and showed that they can win games better than regular methods. Recently, scientists pulled off a groundbreaking experiment, setting up a scenario where Alice and Bob consistently triumph using entangled particles. To perform this, they prepared pairs of qubits in a special way, using lasers and crystals. Making these special pairs was quite tricky, figuring out how to make it work really well. Despite minor imperfections, the experiment showcased remarkable particle behaviour, akin to magic tricks. While impressive, experts emphasise that this concept doesn't violate fundamental scientific principles; instead, it showcases the remarkable properties of particles, particularly entanglement. The importance stems from utilising two seemingly "magical" traits together: one for private communication and the other for quicker problem solving.

References

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Billings, L. (2022) 6 times quantum physics blew our minds in 2022, Scientific American. Available at: https://www.scientificamerican.com/article/6-times-quantum-physics-blew-our-minds-in-2022/?amp=true (Accessed: 25 August 2023).

Ball, P. (2022) Researchers use quantum ‘telepathy’ to win an ‘impossible’ game, Scientific American. Available at: https://www.scientificamerican.com/article/researchers-use-quantum-telepathy-to-win-an-impossible-game/?amp=true (Accessed: 25 August 2023).