Classical teleportation graphic representation
Created by Aidan Stonehouse from Noun Project
Student Guide

Classical teleportation

An exploration of quantum teleportation with coins

Unlike regular information, quantum information is destroyed whenever it is observed or copied. So how can it be sent across networks without being corrupted?

  • 18 coins
  • Six differently colored pairs of sleeves (e.g., folded 3x5 cards glued or stapled shut)
  • Binder clips
Intro

Quantum superpositions are combinations of distinct states: simultaneously up/down, here/there, etc. Unfortunately, the ability to exist in different states at the same time is extremely delicate. Any interaction that provides information about the superposition collapses this special relationship between the states, and any advantage of using quantum technology is lost.

Many applications, like quantum cryptography or distributed quantum computation, require quantum information to be sent from place to place. Normally, to get information from place to place, it’s encoded in something that physically makes the journey, like a written letter or a radio wave. However, interactions with the environment rapidly degrade or collapse quantum information. The solution is not to transmit the quantum information, but to teleport it instead.

Today you will learn to use “classical teleportation” which allows you to send the state of a coin somewhere else without ever finding out what that state is and without ever transporting the coin itself.

Objectives

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

  • Understand that entangled particles have correlated outcomes
  • Describe the need for quantum teleportation, and its advantages
  • Understand when the “quantum particles” (coins) are in superposition vs. in a single, measured state

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

Before the experiment

  • Obtain (or make) several pairs of colored envelopes/sleeves to keep coins in. Your teacher will fill you in on the technique for making sleeves with tape or staples.

  • Obtain 18 coins. It isn’t important for them to all be the same kind.

During the experiment

Classical teleportation uses a pair of correlated coins, a “Near Coin” and a “Far Coin”, to send the state of a “Data Coin” from one place to another without physically transporting it.

  • Take two coins and make sure they have the same side up (both heads or both tails) and place them into two sleeves that are the same color.

  • Clip the sleeves together and toss them in the air so that you don’t know which sleeve is which.

  • Separate the sleeves, being very careful to never turn either of them over. One of these is the Near Coin and the other is the Far Coin. Until we start teleporting in the next activity, it doesn’t matter which is which.

At this point, both coins will have an equal chance of being heads or tails, but whatever one coin is, the other will be the same. The coins are “positively correlated” (if they were always opposites, then they would be negatively correlated). If these coins were quantum particles, we would say that they are “entangled”.

Figure 1: To generate correlation you need to: 1) Place a pair of coins in two sleeves with the same side facing up. 2) Clip them together and toss them in the air. 3) The coins in the two sleeves are now correlated. One is the “Near Coin” and the other is the “Far Coin”.

  • Generate six pairs of correlated coins by following Steps 1-3 above.


  • For each Near/Far pair, predict whether they will be heads or tails.

  • Now look at the Near Coin and make a new prediction about what the Far Coin will be. Record in table. Observe the Far Coin and check your predictions.

Example table:

Teleportation:

It takes three people to teleport a coin: a Sender, a Verifier, and a Receiver. By the end of this procedure the state of the Data Coin has moved onto the Far Coin. Notice that every time you do a teleportation, the correlation between the Near Coin and the Far Coin is destroyed. Also, if the Far Coin is truly far away, the Verifier may need to call the Receiver on the phone.

Figure 2: If the Data and Near Coins are the same, then leave the Far Coin alone. If they're different, turn the Far Coin over. Whatever state the Data Coin was originally in, the Far Coin will be the same. This works whether or not you know what any of the coins are.
Figure 3: To teleport you need to: 1) Place the Data Coin in the sleeve with the Near Coin. 2) Clip it and toss it in the air. 3) Check if they are the same or different, and either leave the Far Coin as it is or turn it over depending on the result. 4) The Far Coin is now in the same state the Data Coin was in.
  • Activity 2:

    Generate six pairs of correlated coins, keep the Near Coin nearby and send the Far Coin far away. Be very careful not to turn the sleeve! The Sender and Verifier stay close to the Near Coin while the Receiver stays close to the Far Coin.

  • The Sender prepares six Data Coins in any way they choose: flipping the coin, selecting heads or tails themselves, using a random number generator with weighted probabilities, etc. The Data Coin states simply represent the information that the Sender wishes to share with the Receiver. The Sender records the state of each coin in the data table below.

    Steps 3-7 are repeated for each trio of coins to teleport the Data Coin’s state to the Far Coin.


  • The Sender places a Data Coin into the sleeve with the Near Coin without showing it to anyone else. The Sender knows the state of the Data Coin, but no one else does.

  • The Verifier clips the sleeve (so that the coins don’t fall out) and throws it in the air so that no one knows which side is up.

  • The Verifier takes the coins out of the sleeve, checks to see if they are “same” or “different”, and records the result in the table below. It does not matter which coin is which, so don’t try to keep track.

  • The Verifier tells the Receiver the result: “same” or “different”.

  • If the Receiver hears “different”, they turn the sleeve containing the Far Coin over. If they hear “same”, then they leave the sleeve alone.

  • The Receiver reveals each of the Far Coins and records the result on the data table below.

Correlation swapping:

Not only is the state of a coin teleported, but its relationships and correlations to other coins are teleported as well. Start with two pairs of correlated coins: “Near/Far pair A” and “Near/Far pair B”. If you use “Far A” as your Data Coin and use pair B to teleport it, then Near A and Far B will now be a correlated pair.

Figure 4: To swap correlation you need to: 1) Start with two pairs of correlated Near/Far Coins, with Far A and Near B close together. 2) Place Far A into the sleeve with Near B without looking at it. 3) Clip it and toss it in the air. 4) Check if they are the same or different, and either leave Far B as it is or turn it over depending on the result. 5) The remaining coins, Near A and Far B, are now correlated.
Activity 3:

  • Generate six pairs of correlated Near/Far Coins. Three of these are the “A pair”, three are the “B pair”.

  • Use “Far Coin A” as a Data Coin and teleport it in the same way. The only difference here is that you need to be careful to never find out what the state of the coin is, so instead of preparing the Data Coin and putting it in the Near Coin sleeve, just “pour” Far A from its sleeve to the sleeve for Near B without looking at it.

  • You should now have a total of three correlated pairs. Verify that each Near A and Far B are now correlated by revealing each pair.

Network teleportation:

It would be impossible to directly connect every computer with every other computer in the world. Instead, everything connects to network hubs which connect with each other. The same thing can be done to make it possible to choose where you want to teleport your coin. The network hubs are collections of differently colored sleeves. If two hubs share a Near/Far pair, then they are connected and can teleport or swap correlation between them.

Figure 5: A network of correlated pairs. Two “nodes” are connected if they share a Near/Far pair. Using correlation swapping and teleportation, a Data Coin can be teleported from any node in the network to any other.


Activity 4:

  • Generate six pairs of correlated Near/Far Coins.

  • Create a network of correlated pairs (see figure 5).

  • Randomly choose which endpoints you want to use to send and receive a Data Coin.

  • Use correlation swapping to correlate the two end points (turning them into a new Near/Far pair).

  • Teleport the Data Coin.

Conclusion
  • What did you learn about the concepts of superposition, entanglement, and teleportation based on this activity?
  • What could you see this principle being used for in the real world?
  • What myths or misconceptions about teleportation has this activity changed for you?

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