Simple diagram of quantum entanglement
Created by Vlad F. Szîrka from Noun Project
Student Guide

Tangled

Entangled vs. separable states

How do we define entanglement and superposition in the context of a quantum computer?

  • Provided in kit:
  • Plastic coins
  • Game boards and scorecards (teacher must print or photocopy for each student - original found in kit)
  • For optional prequel activity:
  • Roughly two dice for every 4 students (can also be done as a class if not enough dice can be obtained)
  • A set of colored pencils for every ~4 students
Intro:

The purpose of this game is to help you learn some of the fundamental terms in quantum computing. Quantum computers are a new kind of computer that may be able to do things that are currently impossible with even the most powerful “regular” supercomputer. To do this they use quantum mechanics, the science of how things work when they are very small. Quantum mechanics shows up in movies and TV all the time but often is presented in misleading ways. This game will teach you about two quantum mechanical ideas: superposition and entanglement.

While regular computers use bits — 0’s or 1’s stored in the computer, quantum computers use qubits. Qubits have a special ability — they can be in a superposition. A superposition is a combination of two different states at the same time. This can happen in quantum mechanics. In a real quantum computer, this might be done with electrons or atoms acting as qubits. We will explore an analogy and use a spinning coin to represent a qubit. The spinning coin has red R (which could represent 1) on one side and yellow Y (which could represent 0) on the other. When it’s spinning, notice that the coin is not R or Y, but both; this is like a qubit in superposition. However, if you “measure” the coin by slapping it on the table, it will no longer be in a superposition, but will be either R or Y. Notice also that a coin doesn’t spin forever, but will stop on its own. This is like how a real qubit behaves. Real qubits can be in a superposition of states, but when they are measured they can only be in one state at a time. Real qubits also tend to “fall over” because the superposition breaks down.

The other important idea in this activity is called entanglement, which is a connection that can exist between two qubits. This connection can come from a physical interaction like a collision, or from two particles getting created from the same source. Entanglement can be explained with math, but we can also see its consequences. If qubits are entangled, measuring one will impact the state of the other one. This is very strange. In our coin analogy (but now with two “entangled” coins) this would mean that if you slapped one coin and got R, the 2nd coin would match, and also be R (for one kind of entanglement). A non-entangled state would not have this matching behavior; if you measure one coin in a non-entangled pair it would have no impact on the second. They would be independent and both would be random.

You will observe both of these ideas in the game Tangle.

Objectives

By the end of this activity, you will be able to:

  • Model superposition using the spinning coin analogy
  • Explain entanglement and distinguish an entangled state from a non-entangled state
  • Understand that entanglement can occur over arbitrary distances
  • Understand that superposition and entanglement are fragile
  • Identify and avoid common misconceptions and hype regarding entanglement

You can create your own objectives too. After reading the introduction, what is your essential question or objective for this activity?


Before the experiment

  • Make sure you have the materials: game rules, scoresheets, game boards and coins.

  • Make sure you’ve read the directions and looked at the game board and scoresheets.

Setting up

It may be a good idea to warm up a bit on your own. Practice spinning your coin toward the center of the board, slapping (“measuring”) your coin, and clapping (stopping) your coin. Observe and get a feel for how measurement results are random. Pair up with a partner and lay out your game boards and score sheets.

During the experiment

Tangle: Game Rules and Directions

You will use a spinning coin to represent a qubit in superposition in this game. Two students, each with a coin, play against each other to explore the difference between entangled qubits and non-entangled qubits.

Before starting, familiarize yourself with the game board and score sheet. Try slapping (“measuring”) and clapping (stopping) your coin. Observe the randomness of your measurements.

  • Fill out the top of your score card and choose the side that you are playing for, either red R (1) or yellow Y (0). This determines what side of the coin you will score points from. Notes: Since the sides are equally likely, there is no advantage to R or Y. Also, a player picking one side does not mean the other player cannot pick the same side. Picking the same side does not mean players get the same score.

  • For each round choose a game state: either non-entangled, entangled state 1: (must match) or entangled state 2: (must anti-match). It is recommended you do one of each game state per game, at least to start. Mark the game state you are using for each round on your score card.

  • For each attempt (tangle) in a round,

    a. Both players spin their coins (like tops) toward the center of their individual game board, from outside its edge. If the coin falls over or goes off the game board etc., immediately pick it up and keep trying to spin it into the middle.

    b. The player with the first coin to reach the middle of their board slaps their coin down, “measuring” it.

    i. If in the non-entangled game state, the second player then immediately slaps their coin down, “measuring” theirs as well.

    ii. If in either of the entangled states, the second player “claps” their coin between their hands, stopping it from spinning.

    • If in the entangled state 1, they flip their coin so that it matches the first player’s coin.
    • If in the state 2, they flip their coin so that it is the opposite of the first player’s coin.

    c. Tangle scoring

    i. The player who first got to the middle gets one skill point.

    ii. If that player’s measured coin matches their chosen side for the round, they get a state point.

    iii. The second player gets no skill point, but if their coin matches their chosen side for the round, they get one state point.

  • Repeat step 3 as many times as necessary to complete the round. There are by default 11 attempts (tangles) per round. At the end of the round, the skill and state points are added, giving a round score. The score has no scientific meaning, and is just for the fun of the game.

  • Repeat steps 2-4 for each game round. The player who wins more rounds wins the game. Note: there are by default 3 rounds per game, with the game state switched each round (recommended) to encourage players to try each game state.

  • Extension: entanglement over arbitrary distances shown by game board separation. Interestingly, entanglement can occur over arbitrary distances. This can be emphasized by separating the game boards farther and farther apart while playing, providing a fun twist.

Analyzing data

Whoever wins more rounds wins.

Conclusion
  1. What do you notice about the relationships between the state rows between player scorecards for non-entangled vs. entangled rounds?
  2. Did the game state rows matter in the game? What do you think would happen if you played many tangles?
  3. Did your choice of R or Y matter in the game? What do you think would happen if you played many rounds?
  4. Based on your observations from this game, define “superposition” and “entanglement” in your own words. Use evidence from this activity to support your definition.
  5. Was your personal essential question answered? If so, what is the answer? If not, what additional information would you need to answer it?

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