One of the first applications of quantum information to cryptography to be discovered is to the creation of money that cannot be copied. Due to the no-cloning principle, which states that there is no procedure that can copy an arbitrary quantum state, we can hope to create perfectly secure money based on quantum information. In this chapter we study how this can be done by following Wiesner’s idea from the 1970s. To analyze the security of Wiesner’s scheme we develop a formalism for general quantum attacks by studying quantum channels, and encounter some limitations of Wiesner’s scheme.

This chapter introduces the basic mathematical formalism for working with quantum information. We discover qubits, or quantum bits, how to combine them using the tensor product, and how to measure them by choosing a basis. We discuss unitary operations, which are elementary transformations on qubits. The chapter ends with a convenient representation of qubits as vectors on the 3-dimensional Bloch sphere, and a useful “cheat sheet,” which summarizes useful definitions and identities.

Terahertz quantum cascade laser sources based on intra-cavity difference frequency generation are currently the only electrically-pumped monolithic semiconductor light sources providing broadly-tunable terahertz output at frequencies up to 6 THz at room temperature. Relying on the active regions with the giant second-order nonlinear susceptibility and the Cherenkov phase matching scheme, these devices demonstrated drastic improvements in performance in the past several years and can now produce narrow-linewidth single-mode terahertz emission that is tunable from below 1 THz to almost 6 THz with power output sufficient for imaging and spectroscopic applications. This chapter provides a comprehensive overview of this device technology

This chapter reviews the applications of terahertz (THz) quantum cascade lasers (QCLs). THz QCLs have come a long way since their first demonstration in 2002. Although still operating at or close to cryogenic temperatures, their applications have been multiplying steadily over the last decade, helped by the availability of compact commercial THz QCL systems and the growing adoption of the THz QCL technology in the THz scientific community. Currently, the key fields of THz QCL applications are imaging, spectroscopy and sensing.

In this chapter, the notion of partons is introduced. Evidence of the substructure of the nucleon is given, and the formalism of the deep inelastic scattering is presented. The form factors and the Bjorken scaling properties are explained in detail. Finally, the parton density functions are presented, and the chapter concludes with the open question of the origin of the proton spin.

The purpose of this chapter is to clearly define the mathematical objects that describe particles of various kinds: bosons (spin-0 and spin-1) or spin-1/2 fermions. Starting from the Schrödinger equation, the Klein–Gordon equation, the Dirac equation and the Maxwell equations are detailed, leading to the description of the associated quantised field – a well-adapted framework to treat states composed of many particles that can be created or annihilated when they interact. The notion of 4-current is introduced, and the quantisation of the various fields is presented. With the Dirac equation, the spinor’s properties are described extensively. The interpretation of the solutions of the Dirac equation in terms of antiparticles and spin or helicity degrees of freedom is then detailed. Helicity and chirality are also treated carefully. Finally, the Maxwell field and the Proca field are described, highlighting their specificities in terms of polarisation degrees of freedom.

This chapter is divided into two parts. The first part introduces the quark model, following more or less the historical developments. It led to an approximate symmetry, based on the SU(3) flavour group, where u, d and s quarks are the three degrees of freedom. The second part introduces the quantum chromodynamics theory (QCD), i.e. the true formal gauge theory of the strong interaction. Here again, the symmetry group is SU(3), but the degrees of freedom are the three quark colours. This symmetry is assumed to be exact, which has consequences on the existence of gluons and their properties, the carriers of the strong interaction at the elementary particle level, briefly mentioned in the previous chapter. The QCD interaction is the first non-Abelian interaction encountered in the book. The non-perturbative regime of QCD is also presented with a short introduction to lattice QCD. A discussion about the colour confinement and the hadronisation of quarks is also given.

Delegated computation is a two-party task where there is a large asymmetry between the two parties: on the one hand, Alice would like to execute a quantum computation, but she does not have a powerful enough quantum computer to execute it. On the other hand, Bob has a quantum computer, but he is not trusted by Alice. Can Alice make sure that Bob executes her computation correctly for her? In this chapter we present three very different approaches to this problem. Each of the approaches is based on a different model for quantum computation, and the chapter also serves as an introduction to these models.

A quantum key distribution (QKD) protocol allows two honest users Alice and Bob to harness the advantages of quantum information processing to generate a shared secret key. The most well-known, and indeed the first QKD protocol that was discovered, is called BB’84, after its inventors Bennett and Brassard and the year in which their paper describing the protocol was published. In this chapter we describe the BB’84 protocol and we introduce the main ideas for showing that the protocol is secure.