Researchers report quantum advantage in a simple cooperation game

Quantum systems hold the promise of tackling some complex problems faster and more efficiently than classical computers. Despite their potential, so far only a limited number of studies have conclusively demonstrated that quantum computers can outperform classical computers on specific tasks. Most of these studies focused on tasks that involve advanced computations, simulations or optimization, which can be difficult for non-experts to grasp.

Researchers at the University of Oxford and the University of Sevilla recently demonstrated a quantum advantage over a classical scenario on a cooperation task called the odd-cycle game. Their paper, published in Physical Review Letters, shows that a team with quantum entanglement can win this game more often than a team without.

“There is a lot of talk about quantum advantage and how quantum systems will revolutionize entire industries, but if you look closely, in many cases, there is no mathematical proof that classical methods definitely cannot find solutions as efficiently as quantum algorithms,” Peter Drmota, first author of the paper, told Phys.org.

“Nevertheless, there are examples where quantum systems can provably perform better than classical systems. Many of those still require advanced mathematics to convey, which is why we have started to look at nonlocal games.”

Compared to many other tasks commonly considered to demonstrate a quantum advantage, the game employed by Drmota and his colleagues can be explained in everyday terms and can be played by anyone in real life. In addition, “solving the game,” which entails finding the best strategy and calculating the corresponding maximum winning probability, is straight-forward.

“We have now realized this game faithfully and without loopholes in a laboratory where players have access to remote entanglement and showed that these players are able to win the game more often with entanglement than without,” said Drmota. “We thus hope to have provided convincing evidence that quantum advantage is real and can be useful.”

The odd-cycle game, the task that the researchers used to demonstrate a quantum advantage, is a nonlocal game. This means that the teammates are each challenged by a referee to respond to a query without communicating to their partner. The team wins if, collectively, their answers are consistent with the winning conditions of the game.

“In the odd-cycle game, each player is asked to assign one of two colors to a plate on a round table with an odd number of seats,” explained Drmota. “The referee randomly assigns them either the same plate or neighboring ones.”

To win the odd-cycle game, the players need to return the same color when they are assigned the same plate and different colors when they are assigned different plates on this table, without knowing which seat was assigned to their partner. Drmota and his colleagues showed that a quantum strategy, which entails that the two players exchange a quantum-entangled state before the game starts, resulted in higher success rates than the best possible classical strategy.

“To demonstrate quantum advantage, we first identified the classical limit to the winning probability,” said Drmota. “Then, we entangled two remote strontium ions (2 m apart), which are controlled by two independent ion trap systems, Alice and Bob. Now, the exciting result is that when they use a quantum strategy instead of the best classical strategy, they win the game significantly more often (with 26 sigma confidence)!”

Measurements performed on the remotely entangled ions reveal correlations between the players that did not exist when employing a classical strategy. With the quantum strategy employed by the researchers, the players’ responses were found to exceed the limit set by classical physics, attaining a clear quantum advantage.

“We believe this is the first time that quantum advantage is shown and explained in a tangible way, accessible to a non-specialist audience,” said Drmota. “Moreover, using the same resources as are employed in the odd-cycle game, we have demonstrated the highest nonlocal fraction between physically separate devices with the detection loophole closed.”

The recent work by this team of researchers shows that quantum systems could outperform classical approaches not only on complex tasks that entail advanced operations, but also on simpler tasks that could be easily described to general audiences. In their next studies, Drmota and his colleagues plan to assess the potential of quantum strategies on other nonlocal cooperative games.

“It is possible to implement different nonlocal games, such as the Magic Square game, which is an example of quantum pseudo-telepathy (where a team with quantum resources can win every time while a team without quantum resources cannot),” added Drmota.

“For this, we will make use of the advanced capabilities developed for a recent experiment in distributed quantum computing. In future studies, we could also increase the number of players to implement the GHZ game, which has been cast eloquently as a TV Game Show ‘Physicists Triumph at Guess My Number’ and serves as a prime example of entanglement-assisted communication—a capability that is poised to have wide-ranging applications in a future quantum internet.”

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