Contract bridge is the chess of card games. You might know it as some stuffy old game your grandparents play, but it requires major brainpower, and preferably an obsession with rules and strategy. So how to make it even geekier? Throw in some quantum mechanics to try to gain a competitive advantage.
The idea here is to use the quantum magic of entangled photons--which are essentially twins, sharing every property--to transmit two bits of information to your bridge partner for the price of one. Understanding how to do this is not an easy task, but it will help elucidate some basic building blocks of quantum information theory. It's also kind of fun to consider whether or not such tactics could ever be allowed in professional sports.
Putting together the nerdier sides of physics and cards has long been the hobby of physicist Marcin Pawlowski of the University of Bristol in the U.K. In 2000, he was a poor college student headed from Poland to China. Trying to save money, he opted to travel overland across the trans-Siberian train route, a trek of several weeks.
“We played bridge a lot on the train,” said Pawlowski. “And I was studying quantum mechanics at the time.”
Bridge is played in teams of two, and a major part of the game involves figuring out how to give your partner information about the cards in your hand using coded signals. Pawlowski realized that quantum particles would allow him to send extra bits of knowledge to his partner during a bridge game. With a team of co-authors and some help from professional bridge players, he wrote a paper about exactly how to do this, which appeared June 12 in Physical Review X.
Bridge is complicated. If you don't know how to play the game, don’t worry. We won’t be delving too deeply into the details just yet. You do need to know that each round of bridge has two main parts; the auction and then the actual gameplay, which is similar to Hearts or Spades.
In the auction phase, players go around and declare the number of hands they expect to win during gameplay. Whichever team ends up with the highest bid sets the trump suit, the suit that can’t be beat. The bids have to be given in a very specific, constrained vocabulary of 38 words or phrases. This isn’t poker and it’s no good bluffing here, because if you set a bid much higher than you can actually win, you will be penalized points.
The bidding round also serves a second, more important function. Through bids, you are communicating to your partner across the table the strength of your hand. The higher you bid, the better you are saying your cards are. Experienced bridge players have added an additional layer of complexity, where certain types of bids actually communicate very specific things to their partners, like how many aces or kings they hold in their hand.
And here’s where the advantage that quantum mechanics offers comes in. Let’s say that two physicists named Alice and Bob decide to enter a bridge tournament. With them, they bring a laser and a special crystal that produces pairs of entangled photons when hit with the laser. Entanglement is a bizarre quantum mechanical property where two particles are perfectly identical. If you measure the characteristics of one of the pair, you immediately know that the other one is exactly the same.
Alice and Bob place their laser-crystal apparatus on the table, and each holds a device capable of measuring different aspects of photons. They fire the laser on the crystal and each take one of the entangled photons. They have agreed beforehand on a convention to pass information to one another using these implements. In bridge, no team is able to have secrets and so the two physicists have to tell everybody what they’re doing (whether or not their opponents understand quantum mechanics is their own problem).
The cards are dealt and the bidding starts. Bob has strong cards and thinks he and Alice can set the highest possible bid and win all the hands during the gameplay round. But he needs to know if Alice’s cards are good enough to support him in the places where his cards are weak. So he uses an agreed-upon convention to ask Alice indirectly about the strength of her cards.
Alice wants to tell Bob about two things: She has the queen in the suit that Bob is strongest in, and she has one ace in another suit. In normal bridge, conveying these two pieces of information would eat up two rounds of bidding. Because each bid must always be higher than the one before, Alice would also drive up the final contract sending these two signals. But then she and Bob might not have strong enough cards, and would end up bidding too high and losing the round and some points. Usually, Alice would just decide to tell Bob about the ace, because it is more powerful.
But now in Quantum Bridge, Alice can give a single bid that secretly has both pieces of information at the same time. She does this with her entangled photon. She can measure the polarization of her photon in one of two ways, let’s call them angle x and angle y. Based on the cards in her hands, she will choose which of these measurements to make. And then she takes the results and does a calculation, calling out a bid based on both the measurement of her photon and her cards.
Bob hears Alice’s bid. He’s only interested in one of the pieces of information. He has enough aces but wants to know if the trump queen is in his partner’s hand or his opponents’. Bob can try to extract the information he wants by measuring a corresponding angle on his entangled photon and combining that result with the bid he heard. With this method, he will correctly deduce the answer 89.5 percent of the time. Pretty sweet.
Even though the result was just one bit of knowledge about Alice’s cards, the partners have an advantage here because they can send two pieces of information at once, and Bob can then decide which is more relevant to him. Their poor non-quantum bridge opponents will fall behind, able to only send one piece of information at a time with their bids.
There’s a lot of chance at work in both this situation and bridge in general. In the card game, there are about 5.36 × 1028 different possible deals, making any particular scenario unlikely. Quantum mechanics, too, relies on probability. We have to take in to account the odds that Alice has some particular cards and the probability that Bob wants to know one piece of information or the other. All in all, Alice and Bob will win about 2 percent more often with their quantum method than if they had just played bridge normally.
All that for a 2 percent advantage? It may not sound like much, but in a card game like bridge, which is played tournament-style with points accumulating over many rounds, this slight benefit will add up in the long run. Even better, Alice and Bob would get to walk into a bridge game and plop down a bunch of physics equipment. Because they are not specifically sharing messages via the photons (everything is communicated through the bids), it wouldn’t really, technically be against the rules.
"I love the idea," said physicist Michael Hall of Griffith University in Australia, who was not involved with the paper. "The physics isn’t all that much new, but what’s really cool is this application to something interesting in the real world."
Hall added that quantum information theorists often make up all sorts of games that help elucidate some principle or method they are researching. But nobody actually plays any of these invented games. In this instance, the researchers were able to show that players could gain a real advantage with quantum mechanics that they wouldn't have using classical techniques.
Would such a thing ever be allowed in the professional bridge world? Most likely not, Pawlowski said. But on some level, that’s what he wants.
“What we would really hope for is that the World Bridge Federation would say, “You can’t do this.” And then they have to mention the quantum information theory in their rules.”
According to the International Olympic Committee, bridge is considered a sport (it and chess are the only two games classified as “mind sports.”) So what Pawlowski and his team are hoping for is a ruling on their method, which would be the first instance of regulating quantum resources in a professional sport. And that might be the geekiest thing ever.
