Theoretical games explore the limits of quantum entanglement

The elusive phenomenon of quantum entanglement could enable unparalleled possibilities, but exactly how powerful are they? CWI researcher Tom Bannink explored cooperative games to assess when entanglement provides an advantage over our classical world. Bannink will defend his PhD thesis today, at the University of Amsterdam.

Publication date: 30-01-2020

The elusive phenomenon of quantum entanglement could enable unparalleled possibilities, but exactly how powerful are they? CWI researcher Tom Bannink explored cooperative games to assess when entanglement provides an advantage over our classical world. Bannink will defend his PhD thesis today, at the University of Amsterdam.

As researchers make important steps to further develop quantum computers, one key element called quantum entanglement has proven to be difficult to grasp. Quantum entanglement appears when particles interact, or share properties with each other, even when the particles are separated by a large distance. While dubbed ‘spooky’ by some researchers, for its elusive character, quantum entanglement could enable unparalleled possibilities. One major question in quantum research however, is exactly how and when quantum mechanics provides an advantage over our classical world.

Non-local games
To better comprehend the powers and limits of quantum entanglement, researchers use theoretical games called non-local games. These games were proposed by physicist John Stewart Bell in the 1960’s, to better understand how quantum entanglement works. While quantum entanglement is a bizarre and puzzling phenomenon, non-local games are pretty straightforward.

In non-local games, two or more players are far away from each other and are not able to communicate. Despite these restrictions, their goal is to win as a group, and not compete with each other.

A referee samples a random input question for each player and sends it to them. Without communicating with each other, the players have to provide an answer back to the referee, who checks to see if they won, as a group. The players are allowed to discuss a strategy before the game starts, but once the referee starts handing out the inputs then the players are on their own.

Quantum advantage
In the quantum scenario they are allowed to share an entangled quantum state and measure this state. It turns out that for some games the players can achieve a higher winning probability when they use quantum entanglement. For some games the quantum advantage is larger than for others.

CWI researcher Tom Bannink identified several types of non-local games for which the advantage is limited. “This research is important because it tells us how and when quantum mechanics provides an advantage over our classical world”, says Bannink. “Although many things are known for 2-player games, in the case of 3 or more players many questions remain about the limits of quantum entanglement.”

Communication complexity
Bannink’s results hold important consequences outside the scope of non-local games, for example in the field of multi-party communication complexity. Bannink: “If non-local games can show unbounded quantum advantages, then we can expect unbounded advantages as well in the amount of communication required in certain communication complexity problems.”

“My PhD research is a small step in better understanding what types of non-local games are interesting to study“, says Bannink. “Many questions remain, though, more research in this direction will definitely be pursued.”

Pascal's triangle
Next to non-local games, Bannink investigated several other topics during his PhD research. Amongst other things, he performed numerical studies of classical sampling algorithms for random graphs, and studied a quantum version of Pascal’s triangle, showing that it can generate a fractal, just like the ‘classical’ Pascal’s triangle.

Quantum software
Funded by the NETWORKS program, Bannink performed his research at QuSoft, the Dutch research centre for quantum software, supervised by Harry Buhrman (CWI, UvA, QuSoft) and Frank den Hollander (Leiden University). QuSoft’s mission is to develop new protocols, algorithms and applications that can be run on small and medium-sized prototypes of a quantum computer. QuSoft’s main focus is the development of quantum software, which requires fundamentally different techniques and approaches from conventional software.

Bannink will defend his thesis Quantum and stochastic processes on 30 January 2020 at the University of Amsterdam. He will continue his career at the start-up company Plumerai, developing binarized neural networks.