An Introductory Path to Quantum Theory: Using Mathematics to Understand the Ideas of Physics

Stephen Bruce Sontz

Benjamin M. Zwickl, Hope J. Hersom

Entanglement is at the heart of emerging technologies such as quantum computing, quantum sensing, and quantum networking.These technologies are developed by interdisciplinary teams of engineers, physicists, software developers, and other scientists.As a result, quantum concepts, such as entanglement, are essential to introduce to a wide range of disciplines.In response, many universities have implemented quantum information science and engineering (QISE) courses for undergraduate students.These QISE courses present quantum concepts to students from diverse disciplines at an introductory level, whereas previously, they were reserved for advanced physics courses.We interviewed students who had recently completed an introductory QISE course to investigate their conceptual and mathematical understanding of entanglement.We found that entanglement was most strongly associated with the idea of correlation between measurements, while only some students productively used the mathematical criterion of whether or not a quantum state was factorable.

Pieter Kok

Massimiliano Malgieri, Pasquale Onorato, Anna De Ambrosis

In this paper we present the results of a research-based teaching-learning sequence on introductory quantum physics based on Feynman's sum over paths approach in the Italian high school.Our study focuses on students' understanding of two founding ideas of quantum physics, wave particle duality and the uncertainty principle.In view of recent research reporting the fragmentation of students' mental models of quantum concepts after initial instruction, we collected and analyzed data using the assessment tools provided by knowledge integration theory.Our results on the group of n ¼ 14 students who performed the final test indicate that the functional explanation of wave particle duality provided by the sum over paths approach may be effective in leading students to build consistent mental models of quantum objects, and in providing them with a unified perspective on both the photon and the electron.Results on the uncertainty principle are less clear cut, as the improvements over traditional instruction appear less significant.Given the low number of students in the sample, this work should be interpreted as a case study, and we do not attempt to draw definitive conclusions.However, our study suggests that (i) the sum over paths approach may deserve more attention from researchers and educators as a possible route to introduce basic concepts of quantum physics in high school, and (ii) more research should be focused not only on the correctness of students' mental models on individual concepts, but also on the ability of students to connect different ideas and experiments related to quantum theory in an organized whole.

Pieter Kok

Julia Kempe, Albert Einstein

This article aims to provide an introductory survey on quantum random walks. Starting from a physical effect to illustrate the main ideas we will introduce quantum random walks, review some of their properties and outline their striking differences to classical walks. We will touch upon both physical effects and computer science applications, introducing some of the main concepts and language of present day quantum information science in this context. We will mention recent developments in this new area and outline some open questions. 1. Overview Ever since the discovery of quantum mechanics people have been puzzled by the counter-intuitive character of the laws of nature. Over time we have learned to accept more and more effects that are unimaginable in a classical Newtonian world. Modern technology exploits quantum effects both to our benefit and detriment—among the memorable examples we should cite laser technology and not omit the atomic bomb. In recent years interest in quantum information theory has been generated by the prospect of employing its laws to design devices of surprising power [1]. New ideas include quantum cryptography [2, 3] and quantum computation. In 1994 Shor [4] discovered a quantum algorithm to factor numbers efficiently (that is in time that grows only polynomically with the length of the number to be factored). This has unleashed a wave of activity across a broad range of disciplines: physics, computer science, mathematics and engineering. This fruitful axis of research has uncovered many new effects that are strikingly different from their classical counterparts, both from the physical point of view as well as from a computer science and communication theory perspective. Over time these communities have gained a greater understanding of the concepts and notions of the other. The idea that information cannot be separated from