Making sense of quantum teleportation: An intervention study on students' conceptions using a diagrammatic approach

TL;DR

This study tackles the gap in pre-university quantum physics education by applying a simplified diagrammatic formalism based on ZX-calculus (QPic) to teach quantum teleportation. Using phenomenography on $n=21$ participants (18 upper-secondary students and 3 pre-service teachers), the authors identify four qualitatively different, hierarchically ordered conceptions of teleportation, shaped by temporality, entanglement, measurement, and diagram interpretation. The findings show that while QPic affords an accessible entry point to modern quantum concepts, it does not automatically resolve deep conceptual hurdles, necessitating carefully designed learning sequences that explicitly connect diagrammatic representations to physical mechanisms. The work offers actionable guidance for educators on how to structure instruction around time, entanglement, and measurement, and underscores the importance of exploring both student and teacher conceptions to improve diagrammatic approaches to quantum physics education.

Abstract

Quantum physics education at the upper-secondary level traditionally follows a historical approach, rarely extending beyond early 20th-century ideas, leaving students unprepared for comprehending modern quantum technologies central to everyday life and many facets of modern industry. To address this gap, we investigated how upper-secondary students and pre-service teachers understand quantum teleportation when taught with a simplified diagrammatic formalism based on the ZX-calculus, which represents quantum processes as diagrams of wires and boxes. Through phenomenographic analysis of video-recorded group work sessions, written responses to exercises, and a group interview, with a total of n=21 participants, we identified an outcome space consisting of four qualitatively different, hierarchically ordered categories of description encapsulating the different ways of experiencing quantum teleportation. The categories revealed that a conceptual progression depends on how one understands the temporality in quantum processes, the role of entanglement in quantum teleportation, the active nature of quantum measurements, and interpretations of mathematical operations in the diagrams. Our findings demonstrate that while a simplified diagrammatic formalism for teaching quantum physics provides an accessible entry point at the upper-secondary level, it does not automatically resolve fundamental conceptual challenges, and requires careful consideration in terms of developing teaching and learning sequences. Finally, these results provide educators with a deeper understanding of conceptual affordances and challenges for designing and improving instruction, whilst also highlighting the need for further exploring how students and teachers alike understand quantum phenomena.

Figures (5)

• Figure 1: An overview of some concepts and rules introduced prior to having students use QPic to discuss quantum teleportation. (a) shows how diagrams can be used to convey connections between objects or describe processes in the real world. (b) introduces the two building blocks used in the version of the formalism relevant in the current study, wires and boxes. A wire shows where something is transported, and boxes show what operation is performed on what is transported. (c) establishes the first fundamental rule: type of wires must match, but they can be connected through a box. (d) establishes the second fundamental rule: only connections matter. (e) shows how to conceptualize time and space in diagrams. Parts of the figure, specifically (a), (b), (d), and (e) are adapted from Coecke2023.
• Figure 2: Establishing a similarity between boxes and mathematical functions. The box represents the function $f(x, y) = x^2 + y$, and produces one output (wire), given two input (wires).
• Figure 3: Introducing the ideas of bending wires and sliding boxes. (a) defines a cup-state as a bent wire with two outputs, and a cap-test as a bent wire with two inputs. (b) defines the 'yanking equation' which follows logically from the second fundamental rule. (c) illustrates that sliding a box through a cup-state results in a rotation by $\pi$ radians. The figure has been adapted from Coecke2023.
• Figure 4: A simple quantum teleportation protocol. An emoji of the Earth is included to signify that the three laboratory locations, separated by dashed gray lines, are separated by a significant distance. In (a), the entire process of teleporting a quantum state (state box with a coffee cup symbol) from Alice to Bob is illustrated, with the inclusion of an 'error' box (a right hand making the peace sign) being introduced in the BSM, and Bob applying the corresponding 'correction' box (a vertically flipped version of the 'error' box, i.e., a left hand making the peace sign) after having received classical information about which Bell state Alice ended up with. In (b), we have the mathematical equivalent system after having applied the 'yanking equation', and (c) shows that Bob ends up with the original state Alice wanted to teleport since his 'correction' box projects his qubit into $|B_{1}\rangle$. The figure has been adapted from Coecke2023.
• Figure 5: Adaptions of the figures in E1 (a) and E2 (b). (a) is adapted from Coecke2023, and (b) is adapted from Bouwmeester1997.