Interactive 2D and 3D Tools for Understanding Qudit State Geometry

This talk presents interactive 2D and 3D visualizations that connect the algebraic structures of qudit states to their geometric representations. Each qudit, defined by probabilities associated with d outcomes, can geometrically be represented as a point on a (d– 1) dimensional simplex. Using this framework, we have built web-based, interactive simplex visualization tools for the states of d=3 “qutrit” states and d=4 two-qubit states in order to make the geometry of qudit spaces directly observable. Users can interact with the system by moving the quantum state within the simplex, dynamically changing the probabilities, and perform simulated measurements to observe the outcomes. The visualizations provides an intuitive geometric interpretation of qudit states and offers an accessible way to explore how quantum state probabilities relate to an underlying Euclidean space geometry.