Tangled

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

If students are not yet familiar with the quantum model of the atom, it may be beneficial to do this prequel lesson before doing activity #4. The prequel lesson is designed to help students understand superposition in the context of the electron, before they move on to qubits. It also helps students understand probability distributions, and how scientists came to create these probability maps (Figure 1) for electron detection location.

Quantum computing:

It is predicted that quantum computing will be able to solve some problems that are intractable with “classical” computers. One of the problems that gets the most attention is encryption; quantum computers, as they become more capable, may be able to crack current encryption methods. As a result, there is tremendous interest in this computing approach and the principles that underlie it. However, there’s also a lot of hype and exaggeration around anything “quantum;” such as depictions in movies and pop culture. This lesson seeks to help build student understanding about some foundational quantum concepts: superposition and entanglement. For students at this level, it’s appropriate to describe quantum mechanics as the science that describes what happens when things are very small (think atoms). Quantum mechanics can have some remarkable consequences, and it is hard for us to visualize and relate since we only have experience with things that are very large by comparison.

Superposition and entanglement in quantum computing:

Quantum computers use qubits rather than bits (1’s and 0’s). What is a qubit? A qubit is a system that can be in a mathematical superposition of two different states at the same time, just like an electron in an atom (see prequel activity above). In a real quantum computer, qubits are implemented using many different physical systems such as electron spins (up vs. down) or energy states of an atom or ion, or the direction in tiny superconducting current loops. In this lesson, a spinning coin is our analogy for this. We can think of the 1 and 0 as yellow (Y) and red (R) of a coin. While the coin is spinning, it is in a superposition of yellow and red. Measurement collapses the superposition and yields an outcome probabilistically. In our particular example, it converts the spinning coin superposition into either yellow or red with equal likelihood.

Entanglement can occur when there are multiple qubits that interact in such a way that their quantum states become linked. This can happen from a physical interaction like a collision, or from sharing a common origin when they are created. Once linked, measuring one qubit collapses the other qubit as well. Depending on the type of entanglement, the linked qubits will either be the same or opposite, but the correlation is definitive. Classically this isn’t possible; multiple simultaneous real coin flips do not impact each other but are independent and their probabilities are given by a product. Teachers and students interested in the mathematical background for superposition and entanglement can find a deeper explanation here.

Something that is remarkable about entanglement behavior is that it appears to work instantly over arbitrary distance. In other words, you can make entangled qubits very far apart and measuring one will still immediately impact the second. This is strange because we know nothing can travel faster than light. Building on this, one very common misconception spread about entanglement is that it may be a way to send signals faster than the speed of light. While it is true that the entanglement will operate immediately over arbitrary distance, it can’t be used to send a signal because the outcome of measurement is probabilistic; you can’t choose the outcome of the first coin and so fix the entangled partner, you only know how the two measurements will be related. These points can be made to students by separating game boards and explaining you could still play while infinitely far apart, but noting that the result of measurement is random and so can’t be used to send messages.

Teacher tips:

• Suggested STEP UP Everyday Actions to incorporate into the activity.
• Consider using whiteboards during discussions, so students have time to brainstorm and work through their ideas before saying them out loud.
• As students experiment, roam around the room to listen in on discussion and notice experiment techniques. If needed, stop the class and call over to a certain group that has hit on an important concept.
• Consider these responsive tools and strategies and/or open ended reflection questions to help push student thinking, and to help students track their thinking during the activity.
• Connect to students’ lives and create opportunities to develop STEM identity using these suggested extensions.
• Allow the work of physicists to come alive by signing up for a virtual visit from a working physicist using APS’ Physicist To-Go program. You can request a quantum physicist to talk about the concepts students learned in this activity!

• Real world connections
  • Sign up for Physicists To-Go to have a scientist talk to your students.
  • Use Elisa Torres Durney’s scientist profile to spark conversations about who does quantum physics
  • Career and Workforce Connections: Quantum Careers lesson (1-2 class periods)
• Drawing, illustrating, presenting content in creative ways
  • Visualize more complex probability distributions through dice rolling and coloring! The teacher and student guides can be found here. Although this activity is intended as a prequel for students who haven’t learned about the quantum model of the atom, it can also be used after the lesson to explore probability distributions more complex than an evenly weighted coin.

**Real world situations/connections can be used as is, or changed to better fit a student’s own community and cultural context.