Surrounded by the high-powered lasers and computer displays of the University of Chicago Pritzker School of Molecular Engineering’s Quantum Education Laboratory (QuantumLab), instructor Danyel Cavazos rapid-fire explained a card game that could change the world.
“So this one is a minus, and minus minus is plus. It is looking good, but then this got messed up, right? So then now this is a minus one, but then you get minus one plus one zero, plus one one, plus one... still two,” Cavazos said, flipping, swapping and quantum entangling the reds and blacks of a deck of playing cards on a laminated sheet of paper.
Cavazos was demonstrating “Entangled and shuffled,” a game he designed to teach the mystifying but important concept of quantum correlation using a dollar store deck of cards. The American Physical Society recently selected the game for inclusion in its yearly PhysicsQuest kit of innovative experiments available for free to middle school teachers across the nation.
PhysicsQuest challenges researchers across the nation to explain this complicated science through cards, poker chips, ping-pong balls and other materials that will be both available and affordable if teachers want to continue the lesson plans in future years.
“Quantum ideas usually sound so complicated. I think if you start hearing about them early on, then maybe we won't have this idea that quantum is just something weird that doesn’t relate to anything important,” Cavazos said. “We want to show kids that quantum is something that they can actually understand.”
Pick a card, any card
Games are an ideal vehicle for introducing complicated concepts to children, Cavazos said. It’s how they already learn.
“The easiest way for me to introduce probability to a kid is through a game. What's the chance that you will win if you roll a die? What's the chance that you will roll an even number?” he said. “What we’ve done is take that concept to the quantum world.”
In “Entangled and shuffled,” which is also available to play online, students lay four cards in a line on a laminated sheet of paper. The sheet has four slots for cards, with lines connecting different slots. Slots connected by a line correspond to the outcomes of measuring pairs of entangled states, an important concept making quantum computers, biosensors and other technological innovations possible.
If the colors of two cards linked by a line match, that’s worth one point. If they don’t match, that’s minus one. And the game is off, with students laughing, flipping, scrambling and adding, trying to get the total tally higher than two.
Spoiler alert
A bit of an unfortunate spoiler for frustrated middle schoolers: It’s impossible to get higher than two. With playing cards, that is. Entangled photons do just fine.
Although "Entangled and shuffled” uses cards and paper rather than lasers and crystals, the math is identical to an experiment known as a Bell’s inequality measurement, which uses entangled particles such as photons to test the strength of quantum correlations. The experiment won the 2022 Nobel Prize in Physics.
“They did, literally, this experiment with photons,” Cavazos said. “The math behind it is exactly the same as the game. You have to calculate the expectation values and you put them together with that extra minus sign.”
To illustrate, Cavazos turned a dial on a QuantumLab laser array, triggering the actual quantum experiment he explained with cards. Using classical objects like cards, the students couldn’t get beyond 2. Using a quantum display, Cavazos reached 2.638.
This is possible because, instead of just having two states (on or off, red or black) quantum mechanics allows for a third possibility where these states are entangled, with no determined identities until they are measured. It finds a way of being both and neither of the possible states at the same time – not “on” or “off” but “on/off,” or red/black for the cards. This probabilistic wiggle room breaks through the barrier that simple objects like cards couldn’t crack.
With quantum’s growing profile in the science, technology and the economy, it’s important to introduce these concepts early on, Cavazos said.
“If kids play this game and they feel like they understand it, then when someone describes the physics experiment that won the 2022 Nobel Prize, they can say, ‘Oh yeah, exactly, just like that game,’” he said.
2025 International Year of Quantum Science and Technology
The United Nations declared 2025 the International Year of Quantum to mark a century of progress in quantum science and engineering. The University of Chicago and its partners join the celebration of the groundbreaking fields that continue to positively impact lives around the world.
