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Quantum Measurements

Compare quantum and classical measurements of a spinning coin with an interactive simulation.

This is a simulation of a coin that spins indefinitely (rather than a flipped coin that will eventually come to rest on a surface) using red and blue colors to distinguish between the head and tail sides.

Initial development by David Kirkby for the 2015 "Quantum Physics" course (113A) at the University of California, Irvine.

This is an open source project, released under an MIT license, that builds on other open source projects: bootstrap, jquery, d3js. Suggestions for improvement are welcome: please create an issue to start the discussion.

Instructor's Guide

High-School

This worksheet (google doc) introduces probabilistic models of classical and quantum coins with simple hands-on activities. Students are then prepared to interact with the simulation, understand the graph, and discover the role of measurement in a quantum system.

This material was initially developed for a 2017 UC Irvine COSMOS guest lecture. Contact dkirkby@uci.edu for details if you want to try this. Allow about one hour to complete this worksheet.

Undergraduate

These flow charts might be helpful for discussing the differences between classical and quantum measurements, and then relating the quantum coin to measurements involving stationary states or a more general formulation of quantum measurement.

Here is a suggested student activity that will take about 30 minutes to complete:

  1. Visit https://dkirkby.github.io/quantum-coin/ on your laptop, tablet, or phone.

    This is a simulation of a coin that spins indefinitely (rather than a flipped coin that will eventually come to rest on a surface) using red and blue colors to distinguish between the head and tail sides.

  2. Leave the simulation set to ‘Classical’ and play with its controls until you get a feel for what is going on. Discuss with each other what ‘measurement’ means according to the simulation.

  3. Now change the setting to ‘Quantum’. Discuss with each other the differences between the classical and quantum coins and anything you find confusing?

  4. Study the flowchart below which represents the classical coin, then draw an analogous flowchart for the quantum coin on your whiteboard. (Hint: some parts of the flowchart stay the same.)

Classical Coin Flowchart

  1. Discuss with each other whether it is possible to make the “spinning” quantum coin spend more time in one state than the other? Could you keep it in one state indefinitely?

  2. Each quantum measurement generates a green dot: how does the dot’s position determine the outcome of the measurement?