Highlights from the Special Collections of AJP and TPT on Teaching About Quantum

Before taking a single physics class, each person has years of experience understanding how objects move through space and time. These spatial intuitions are invaluable aids assisting everyone, from starting students to experienced researchers, as we navigate the formulas, coordinate systems, and abstract concepts of classical physics. With quantum mechanics we are not so fortunate. The description and evolution of quantum states in conventional presentations is heavily formulaic and algebraic, making sparse use of our abilities for visual intuition that are such useful aids to our understanding. In this talk we will discuss some remedies for this situation by presenting visualization tools for teaching and learning about quantum states. Examples will include an improvement to the Bloch sphere that allows direct visualization of the linear algebra representations of single-qubit pure and mixed states, a map of two-qubit states that enables one to see the degree of qubit entanglement, and some general spatial intuitions that apply to many-qubit states. These visual tools can help free one's thinking about quantum states from the coordinate-system formalism that often dominates their description and can be used across multiple educational levels: from being visual aids requiring no mathematics for the starting student to providing geometrically intuitive shortcuts for the more involved calculations of advanced students.