Games are useful tools for introducing new concepts to students. This paper describes a competitive two-player game for sophomore students in a modern physics survey course or junior/senior students in an introductory quantum mechanics course to build intuition and quantitative understanding of the probabilistic nature of quantum measurements in two-level systems such as qubits or the Stern–Gerlach experiment. The goal of the game is to guess a quantum state secretly chosen from a given set in the fewest number of measurements. It uses 20-sided dice or other classical random number generators to simulate quantum measurements. The Bloch vector formalism is introduced to give a geometric description of the quantum states and measurement outcomes. Several ready-to-use sets of quantum states are given, so readers can jump right in and try the game themselves without any prior knowledge of quantum mechanics. More advanced students can also use the game in suggested follow-up exercises to deepen students' understanding of quantum measurements and their statistical description.
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Statistically speaking, the simulation represents three independent Bernoulli processes with probabilities , and , where the values of the probabilities are related to each other by the normalization constraint that the length of the Bloch vector equals one. This constraint complicates the problem of estimating the state from measurement data—naïve application of Eqs. (4) and (5) can yield nonphysical estimates of the state that violate the normalization constraint .
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