Shall we play a game?
What do games have to do with quantum mechanics and communication? A lot, actually. Using just paper and pen, mathematical logic games like the magic square game mimic the way a MAC operates, Smith explained.
Here’s how the magic square game works: two players (we’ll call them Alice and Bob) have to fill a three-by-three square—Alice with plus signs and Bob with negative signs—while a single referee decides which row or column they are filling out. Alice needs to have an even number of plus signs in each row. Bob needs an odd number of negative signs in each column.
But there’s a catch: Alice and Bob are separated. You can think of them as being separated by a wall, Smith said. They cannot communicate, which means that one won’t know which column and the other won’t know which row they are filling out at any time.
If Alice or Bob fails, the information is wiped out, which mimics noise in a MAC communication system. Even if our imaginary players agree on a strategy ahead of time, the best Alice and Bob can do is win eight out of nine games, Smith explained.
In quantum mechanics, particles exist in all possible states at once until you observe them. When particles physically interact with each other they can become entangled. Entangled particles are connected forever, until noise or measurement disrupt them. Whatever happens to one instantaneously affects the other, even if they are separated by great distances.
With entanglement Alice and Bob can peak around the wall. Though they cannot communicate with each other, Alice and Bob can use the quantum correlations to win with certainty, Smith said. Apply that to a MAC and you could create a channel that can handle more data, with much less noise or interference, he added.
Coding for the future
Furthermore, the MAC’s capacity increased regardless of how much entanglement is created. The Smith Group found that even creating a little bit of entanglement can improve the rates on a classical system, i.e. in principle we could apply new quantum tools to our existing communication networks and improve them.
And they also found our classical MACs are more complex than we thought. Mathematicians had believed that without quantum mechanics, it was possible to find single, computable formula that let’s Alice and Bob win the game every time. Smith and his team found that finding a perfect strategy for Alice and Bob is NP-hard—that is, finding a solution would take such an incredibly long time as to be impractical.
This work is just the start. With this knowledge, the Smith Theory Group can start working on finding the limits on coding strategies for these MACS, both classically and with quantum entanglement.
This research was published in Nature Communications on March 20, and was funded by the National Science Foundation Physics Frontier Center grant and the CAREER Award.
Written by Rebecca Jacobson