Classical teleportation

There are four main activities, each with specific rules and procedures outlined in the student guide, linked above. Please review the explanations provided here and consult the student guide for detailed steps on how to carry out the activity.

1. Generating correlation
2. Classical teleportation

The first two are self-contained enough that if you run out of time (or only budgeted a little time), then you can stop there.

1. Correlation swapping
2. Network teleportation

The third and fourth activities are about how an actual quantum network is run.

Two of the procedures, the “same/different measurement” and the “correlation generation”, look very similar and are easy to confuse, so be sure to make the distinction clear. When a correlated pair is created and then immediately used to teleport a coin, students tend to lose track of what’s happening (“Why are we clipping and flipping these coins again?”). To avoid that, first generate many correlated pairs, and then use them to teleport.

Generating correlation

In the activity, the students will create correlated pairs of coins, guess whether they’ll be heads or tails, then reveal one, and guess again. The point this is trying to get across is that “correlated” means “random, but the same”. For example, if all of the coins are always heads, then they aren’t correlated. Correlation implies that learning about one tells you something about the other, but if you know they’re always heads, then there’s nothing to learn.

Classical teleportation

A single bit can be used to describe the outcome of a coin flip, because there are only two options on a coin (heads/tails which can code for 0/1). However, if you want to describe how the coin behaves over many flips, i.e. the probability distribution of the coin (like 70% heads, 30% tails for a weighted coin), you'll need to transmit a lot more information. Thus, it would actually take many classical bits to accurately transmit a probability distribution like 30/70. This is where quantum teleportation is extra cool and powerful: using only an entangled pair and two classical bits, you can transmit both the inherent probability of the particle AND the quantum phase information. Instead of sending the data classically, the entanglement carries the structure of the state, and the two classical bits tell the receiver what transformation they must perform to make them match completely. We see this in this activity in the fact that we know the coins will match, but we don’t know the state they are in. Hopefully doing the activity will illustrate these concepts more fully. This is difficult to comprehend and may take many attempts. Feel free to learn with the students and be open about the fact it is challenging.

Correlation swapping

Let’s say particle A is entangled with particle B, and particle C is entangled with particle D. If we perform a special kind of measurement (called a Bell measurement) on B and C, then A and D become entangled — even though they never met. This is called correlation swapping, or entanglement teleportation, and it’s the “repeater step” that allows us to separate our entangled pair over greater distances. This "repeater step" isn’t used to transmit the data itself, but it uses the same mechanism (entanglement) to transport the correlation. After we’ve created the desired distance between our correlated pairs, we can use teleportation between the pairs to transmit the data.

Network teleportation

Unlike regular repeaters (which listen for a signal, then repeat and amplify it) correlation swapping can be done in any order. Students may notice that when teleporting across a network, they’re doing a chain of correlation swaps (which is the same as a chain of teleportation). The only relevant piece of information that the students will need to keep track of is the total number of “different” results they get; an odd number of results means “turn the Far Coin over” and an even number means “leave it alone”, since turning the coin over twice is the same as leaving it alone.

During this activity you may need more than the six recommended sleeve pairs if you want to create a non-trivial network (with a couple intermediate hubs and multiple endpoints).

Students 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

*It is important to understand that student goals may be different and unique from the lesson goals. We recommend leaving room for students to set their own goals for each activity.

Collecting data

This experience is about understanding and playing around with a protocol used for quantum communication. When it works, the result is always the same: the state of the Data Coin gets to the intended destination. All data collection is done with this aim in mind. See the student guide to walk through the activities.

Understanding Activity 2:

For teachers (and students) trying to track when the coin sleeves represent quantum particles that are in superposition vs. in a collapsed, observed state, the following may be helpful:

1) First, we line up two coins in the same state (both heads up, or both tails up). In our experiment, we have to look at our coins to know that they line up, but in a lab, we have ways of creating entangled particles that don’t involve observing the state of the particle, so we don’t count this step as collapsing the wave function. For example, if we can make a zero-spin parent particle decay into two daughter particles, we know that the two daughter particles’ spins will be opposite of each other (anti-correlated), but we can’t say which is positive and which is negative. The relationship between the two particles (and the two coins) remains intact even when we increase their physical separation. Status of Near and Far Coins: in superposition, and correlated.

2 - 3) In our experiment, we write down the state of the Data Coin before we entangle it so that we can check that its state has been successfully transmitted by the end, and that the experiment works. But in real life, we wouldn’t observe the state of the quantum data before entangling it with the nearby particle. Instead of transmitting a single state, we would be transmitting a probability distribution, or the whole quantum state. Status of the Data Coin: in superposition.

4) Now we’ve flipped the Data Coin with the Near Coin, representing the entanglement of the two particles. Status of the Data Coin and Near Coin: still in superposition, and either correlated or anti-correlated with each other (we don’t know which yet). Status of the Far Coin: In superposition, but no longer correlated with the Near Coin.

5 - 6) When the Verifier removes the coins to check their states, their superposition of both the Near Coin and the Data coin collapses, and we know the state of both coins. The correlation between the Near Coin and the Far Coin has also been broken, but this is a necessary step. Remember, we want the Far Coin to have the same state as the Data Coin, rather than the Near Coin. After observing the relationship between the Near Coin and the Data Coin, we know the transformation that we will need to perform on the Far Coin to make it match the Data Coin.

7) Based on the result of the observation in 6 (the coins are the same vs. different), the Receiver is able to complete the transformation on the Far Coin (either flipping it or keeping it the same). This does NOT require an observation! That means we’ve been able to completely transfer the state from the Data Coin to the Far Coin without ever collapsing the wave function of the Far Coin!

8) If the experiment went correctly, then step 8 is merely a “checking” step. We know the Far Coin’s state because of its relationship with the Data Coin and the Near Coin. But once we “check” on the coin and record its state, we’ve officially observed it, and the wave function of the representative particle has collapsed.