The retrieval of phases from intensity measurements is a key process in many fields in science, from optical microscopy to x-ray crystallography. Here we study phase retrieval of a one-dimensional multi-phase object that is illuminated by quantum states of light. We generalize the iterative Gerchberg-Saxton algorithm to photon correlation measurements on the output plane, rather than the standard intensity measurements. We report a numerical comparison of classical and quantum phase retrieval of a small one-dimensional object of discrete phases from its far-field diffraction. While the classical algorithm was ambiguous and often converged to wrong solutions, quantum light produced a unique reconstruction with smaller errors and faster convergence. We attribute these improvements to a larger Hilbert space that constrains the algorithm.

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Background Virtual reality (VR) is considered a promising approach to support learning. An instructional design is essential to optimize cognitive processes. Studies show that VR has unique instructional and pedagogical requirements. Objectives To evaluate the effectiveness and applicability of the modality principle, which was previously validated in 2D classic multimedia, for learning with VR. The modality principle states that multimedia information presented as spoken narration is superior to on‐screen text. Methods A prospective experimental study with two compared conditions of instruction: VR‐based learning guided by on‐screen text (n = 34) versus spoken narration (n = 28). Students' cognitive learning experiences were captured by eye‐tracking and electrodermal activity (EDA). In addition, students' knowledge was evaluated using a pre–post knowledge test. Results and Conclusions Overall, there was no significant difference in knowledge retention between the participants who learned with on‐screen text compared to spoken narration. However, results from the eye‐tracking analysis showed that students who learned with the on‐screen text devoted longer visual attention toward important learning activity areas of interest, suggesting a better ability to discern between relevant and irrelevant information. Conversely, students who learned with the spoken narration expressed significantly more EDA peak responses, proposing a higher cognitive load. Implications This study outlines that while learning with VR was effective, the modality principle might not apply to learning with VR. Moreover, the analysis of the learning process suggests even an inverse effect, favouring the provision of instructional scaffolds as on‐screen text. Future research should evaluate this effect on long‐term knowledge retention.