Playing games with quantum interference

As Richard Feynman famously put it, “the double slit experiment is absolutely impossible to explain in a classical way and contains the heart of quantum mechanics. In reality it contains the only mystery.”

Indeed, in this experiment, a quantum particle behaves as if it were in two different locations at the same time, exhibiting paradigmatic wave-like phenomena such as interference. However, it was later noted that multi-slit experiments show that the degree of delocalization of quantum particles has its limits, and that quantum particles, in a sense, cannot be delocalized at more than two locations at the same time. This limitation has created a puzzle that has not been fully solved to this day. Researchers from the University of Vienna and IQOQI-Vienna (Austrian Academy of Sciences) have taken an important step to understand this problem by reformulating interference experiments in terms of information theoretical games. Their analysis, recently published in the journal Quantum, provides an intuitive way to think about interference phenomena and their limitations, paving the way for solving the above puzzle.

One of the most striking features of quantum mechanics is the superposition principle. This principle is most easily illustrated through the double slit experiment, where a particle is sent through a plate pierced with two slits. According to our everyday intuitions, you might expect the particle to always pass through one slit or through the other. However, quantum mechanics implies that in a sense the particle can pass through both slits at the same time, that is, it can be in a superposition of two locations at the same time. This possibility underlies the phenomenon of quantum interference, ie the striking wave-like behavior of quantum particles. Is there now a way to quantify the extent to which quantum particles can be delocalized? Does quantum theory allow particles to traverse more than two paths at the same time? To understand these questions, physicists analyzed “multi-slit experiments,” which differ from the double slit experiment only in the number of slits: for example, a three slit experiment involves a particle being sent through three slits.

You might think that if a quantum particle can pass through two slits at the same time, it must also be able to pass through three, four, or any number of slits at the same time. Surprisingly, it was immediately noted that any pattern obtained in multi-slit experiments can be explained by the particle always passing through up to two slits at a time. While this feature is fully understood mathematically, the following questions remain unanswered: Is there a physical reason for the apparent asymmetry between the double-slotted experiment and the multi-slotted experiments? What is the basis for this somewhat arbitrary restriction on the “delocalization” of quantum particles?

In their recent work, Sebastian Horvat and Borivoje Dakić, researchers from the University of Vienna and IQOQI-Vienna (Austrian Academy of Sciences), took an important step to understand this problem by tackling it with information theory. Namely, they have reformulated interference phenomena and multi-split experiments in terms of “parity games”, the simplest example of which is illustrated in the figure. The game involves two players, Alice and Bob, who are separated from each other by a wall pierced with four pairs of pipes. Each pair of tubes can be straight or twisted, and the number of twisted pairs is unknown to both Alice and Bob. Alice also has a number of marbles that she can tap through the tubes to Bob; the players can use these marbles to learn about the structure of the tubes.

The aim of the game is for the players to work together and find out if the total number of pairs twisted is odd or even, using as few marbles as possible. Now suppose Alice throws a marble through one of the tubes, for example through the second. Bob can then easily deduce whether the first pair of tubes are straight or twisted by simply checking if the marble fell through the second tube or through the first. Similarly, if Alice has four marbles at her disposal, she can blow them all through the right tube of each pair (as is the case in the picture). Bob can then easily deduce the number of pairs turned, and thus whether this number is odd or even, and thus win the game. However, if the number of tube pairs is greater than the number of marbles Alice has, the game cannot be won, as there will always be at least one pair of tubes that Bob cannot collect any information about. To win the game, therefore, the players must use as many marbles as there are pairs of tubes.

On the other hand, quantum mechanics, and more specifically the superposition principle, allows the players to win the game illustrated in the figure by using only two “quantum marbles”! One way to understand where this improvement is coming from is to remember, as mentioned earlier, that a quantum particle can “pass through two locations at the same time.” Thus, two quantum marbles can “pass through four locations simultaneously”, mimicking the behavior of four common (classic) marbles. “In this game, marbles behave analogously to tokens that can be inserted through the tubes. When Alice puts a regular classic marble in it, it’s like she put in 1 cent.

On the other hand, since quantum theory allows marbles to “pass through 2 tubes at the same time,” each quantum marble is worth 2 cents. The value of the tokens is additive: to win the game, Alice can, for example, insert 4 classic marbles or 2 quantum marbles, as the total token value is equal to 4 tokens in both cases, ”explains Sebastian Horvat. However, keep in mind that a quantum particle does not can pass more than two locations at the same time: this is reflected in the fact that Alice and Bob cannot win the game by using less than two quantum marbles. game, the number of quantum marbles sent by Alice must be equal to at least half of the total number of tube pairs.

In their work, the researchers analyzed more general formulations of this game and studied the performance of the players depending on the number of particles and whether the particles are classical, quantum or more general and hypothetical. Borivoje Dakić adds, “These hypothetical particles have higher information processing power, that is, their corresponding tokens are valid for more than 2 cents. It is not clear why nature would prefer classical and quantum particles over these hypothetical: this is something we still have to study in the future. “

Overall, parity games provide an alternative description of quantum interference within a more general and intuitive framework, which will hopefully shed light on new features of quantum superposition, similar to how the study of quantum entanglement has been deepened by the formulation of the so-called “non-local games. . ”