Your Basis, My Basis
Alice Flarend, Bob Hilborn · 2022
Abstract This chapter introduces important symbolic manipulations of quantum states—in particular, changing the basis states used to describe a quantum state. The inner product between state vectors plays a crucial role in those manipulations. That process is critical in extracting information from quantum states and appears in almost every quantum algorithm. Alice and Bob use a simple do-it-at-home experiment with polarized light and polarizing materials to illustrate how changing basis states explains what otherwise seems like a mysterious effect. To illustrate how these basic quantum principles can be applied to important information science situations, they introduce quantum encryption methods and how quantum physics principles allow them to detect if someone is eavesdropping on their communications channel. The methods Bob and Alice introduce, though relatively simple mathematically, enable them to estimate the probability that they will be able to detect the presence of an eavesdropper, a critical issue in cryptography.