Colored liquid spreading through water can be described as a random walk. A new study shows that the quantum version of a random walk can give rise to a bizarre paradox where two losing games can combine to become a winning one.

Two losing games can add up to a winning one, according to a concept called Parrondo's paradox.

Now, physicists have shown that this paradox also exists in the realm of quantum mechanics, the rules that govern subatomic particles. And it could lead to faster algorithms for future quantum computers. [The Mysterious Physics of 7 Everyday Things]

Physicist Juan Parrondo first described the paradox in 1997 to explain how randomness can drive ratchets — asymmetrical, saw-toothed gears that allow motion in one direction but not the other. The paradox is relevant in physics, biology, and even economics and finance.

A simple example of Parrondo's paradox can be illustrated with a coin-flipping game. Say you bet a dollar on flipping a weighted coin that gives you slightly less than a 50-percent chance of guessing the right side. Over the long run, you would lose.

Now play a second game. If the number of dollars you have is a multiple of 3, you flip a weighted coin with a slightly less than 10-percent chance of winning. So nine out of 10 of those flips would lose. Otherwise, you get to flip a coin with just under a 75-percent chance of winning, meaning you'd win three out of four of those flips. It turns out that, as in the first game, you would lose over time.

But if you play these two games one after another in a random sequence, your overall odds go up. Play enough times, and you'll actually end up richer.

"Parrondo's paradox explains so many things in the classical world," said study co-author Colin Benjamin, a physicist at India's National Institute of Science Education and Research (NISER). But "can we see it in the quantum world?"

In biology, for example, quantum ratcheting describes how ions, or charged molecules or atoms, pass through cell membranes. To understand this behavior, researchers can use simple, easy-to-simulate models based on quantum versions of Parrondo's paradox, said David Meyer, a mathematician at the University of California, San Diego, who was not involved in the research.

One way to model the random sequence of games that gives rise to the paradox is with a random walk, which describes haphazard behavior such as the motion of jiggling microscopic particles or the circuitous path of a photon when it emerges from the sun's core. [See Gorgeous Images of the Sun's Corona in Simulations]

You can think of a random walk as using a coin flip to determine whether you step to the left or right. Over time, you might end up farther to the left or the right of where you started. In the case of Parrondo's paradox, stepping left or right represents playing the first game or the second.

For a quantum random walk, you can determine the sequence of gameplay with a quantum coin, which gives not only heads or tails but also both at the same time.

It turns out, however, that a single, two-sided quantum coin doesn't give rise to Parrondo's paradox. Instead, Benjamin said, you need two quantum coins, as he and Jishnu Rajendran, a former graduate student at NISER, showed in a theoretical paper published in February 2018 in the journal Royal Society Open Science. With two coins, you step left or right only when both show heads or tails. If each coin shows the opposite, you wait until the next flip.

More recently, in an analysis published this June in the journal Europhysics Letters, the researchers showed that the paradox also arises when a single quantum coin is used — but only if you allow the possibility for it to land on its side. (If the coin lands on its side, you wait for another flip.)

Using these two ways of generating quantum random walks, the researchers found games that led to Parrondo's paradox — a proof of principle that a quantum version of the paradox does indeed exist, Benjamin said.

The paradox also has behaviors similar to those of the quantum search algorithms being designed for tomorrow's quantum computers, which could tackle calculations that are impossible for normal computers, physicists say. After taking a quantum random walk, you have a much higher chance of ending up far from your starting point than if you took a classical random walk. In that way, quantum walks disperse faster, potentially leading to faster search algorithms, the researchers said.

"If you build an algorithm that works on a quantum principle or random walk, it will take much less time to execute," Benjamin said.

Editor's Note: This story was updated to clarify that Jishnu Rajendran is no longer a graduate student at NISER.

Originally published on Live Science.