# Secure Quantum Communication Technologies and Systems: From Labs to Markets
## 2 Quantum Key Distribution Systems and Networks
### Discrete Variable Systems  
The discrete variable (DV) approach to QKD has been extensively studied, and most of the testbeds and available commercial devices are of this kind. The underlying idea is that since it is well-known that in quantum mechanical systems any measurement perturbs the system, this feature can be exploited to understand if someone is trying to steal data from the channel. BB84 is an example of discrete variable quantum key distribution (DV-QKD), where a finite number of polarization bases are used to encode bits. The sender ([PERSON]) generates a random bit (i.e., either a \"0\" or a \"1\") and encodes it in one of two different bases, over a given physical parameter of a photon (typically, polarization). The first basis is used to encode \"0\" bits and the second base for \"1\" bits. Since the receiver ([PERSON]) does not know the sender's basis selection, he measures (after propagation in an optical fiber link) the polarization of the incoming photons by randomly using one of the two possible bases. If he uses the same base as the sender, he will measure the correct bit value; conversely, if he chooses the wrong base, the result of the measurement will give the correct result only with 50% probability. After a long sequence of photons has been exchanged, [PERSON] and [PERSON] compare the bases they have employed to encode and measure each photon, respectively, by communicating via a classical channel. They keep only the bits generated and detected with a matched base, which are said to constitute the sifted keys. In an ideal system without noise, imperfections, and disturbances, the sifted keys are identical and can be used as a private key. Typically, the two polarization bases used by the sender are selected by a polarizer and are rotated 45\({}^{\circ}\) about each other. They are called rectilinear (0\({}^{\circ}\), 90\({}^{\circ}\)) and diagonal (45\({}^{\circ}\), 135\({}^{\circ}\)) bases. At the receiver, a polarization beam splitter (PBS) transforms the polarization encoding into a spatial encoding, so that the photons can be detected using two separate photon avalanche photodetectors (SPAD). Starting from the BB84 protocol, many variants of QKD protocols have been proposed over the years, but the basic concept has remained the same. We briefly examine some of these protocols without extensively describing them. Incrementally moving from the original BB84 protocol, it is worth noticing that it can be implemented using physical features that differ from polarization. For example, phase encoding is an alternative [2]; the sender uses a Mach-Zehnder interferometer (MZI) to introduce one out of four alternative phase shifts (\(\phi_{\mathrm{a}}\)), for example \(\phi_{\mathrm{a}}=\left[ \begin{array}{cc}0,&\frac{\pi}{2},\pi\frac{3}{2}\pi \end{array} \right]\), with the first two linked to a \"0\" bit and the latter to a \"1\" bit. The receiver uses a second MZI to randomly introduce one out of two phase shifts (\(\phi_{\mathrm{b}}\)), for example \(\phi_{\mathrm{b}}=\left[ \begin{array}{cc}0,&\frac{\pi}{2}\end{array} \right]\). The transformation from phase to spatial encoding at the receiver is made on the basis of the differential phase \(\Delta\phi=\phi_{\mathrm{a}}-\phi_{\mathrm{b}}\). Similarly, encoding exploiting the photon spin was proposed in [3,4]. In 1991, the E91 protocols were proposed [5]. This system is similar to BB84 but it uses entangled photons to guarantee the security of the communication, relying on the no-cloning theorem proven by [PERSON] in 1992 [6]. E91 still uses the polarization to encode information and the same BB84 mechanism to statistically detect an eavesdropper. Entangled photon pairs are distributed among communicating partners, which choose a measurement basis; if two partners choose the same basis, the measured bit will be equal, otherwise the bit is discarded.