Chapter 15 - Quantum Key Distribution

Abstract

This chapter is devoted to the fundamentals of quantum key distribution (QKD). The chapter starts with a description of key differences between conventional cryptography and QKD. In the section on QKD basics, after a historical overview, we review different QKD types. We then describe two fundamental theorems on which QKD relies, namely the no-cloning theorem and the theorem of the inability to unambiguously distinguish nonorthogonal quantum states. In the section on discrete variable QKD systems we describe BB84, B92, Ekert (E91), Einstein–Podolski–Rosen, and time-phase encoding protocols. In the section on QKD security, the secret-key rate (SKR) is represented as the product of raw key rate and fractional rate. Moreover, the generic expression for the fractional rate is provided, followed by a description of different eavesdropping strategies, including individual (independent or incoherent) attacks, collective attacks, coherent attacks, and quantum hacking/side-channel attacks. For individual and coherent attacks, the corresponding secrete fraction expressions are provided. After that, the decoy-state protocol is described together with corresponding SKR calculation. Next, the key concepts for measurement device-independent (MDI)-QKD protocols are introduced, including polarization-based and time-phase encoding-based MDI-QKD protocols as well as secrecy fraction calculation. Twin-field QKD protocols as further described, whose performance is evaluated against decoy-state and MDI-QKD protocols. The focus is then moved to the information reconciliation and privacy amplification steps. To facilitate the description of continuous variable (CV)-QKD protocols, the fundamentals of quantum optics and Gaussian information theory are introduced first. The topics include quadrature operators, Gaussian and squeezed states, Gaussian transformation, generation of quantum states, thermal decomposition of Gaussian states, two-mode Gaussian states, and measurements on Gaussian states. In the section on CV-QKD protocols, homodyne and heterodyne detection schemes are described first, following a brief description of squeezed states-based protocols. Given that the coherent states are much easier to generate and manipulate, the coherent states-based protocols are described in detail. For the lossy transmission channel, the corresponding covariance matrices are derived for both homodyne and coherent detection schemes, followed by SKR derivation for prepare-and-measure Gaussian modulation (GM)-based CV-QKD. Illustrative SKR results are provided for GM-based CV-QKD schemes. Next, relevant concluding remarks are provided, followed by a set of problems.