# Secure Quantum Communication Technologies and Systems: From Labs to Markets
## 2 Quantum Key Distribution Systems and Networks
### Continuous Variable Systems  
DV-QKD systems require ad-hoc devices to operate, such as single-photon detectors and single-photon sources. This is a major obstacle to industrialization due to small production volumes (at least during the initial phases of introduction on the market_ and the need to setup a dedicated supply chain. Moreover, the efficient generation, detection, and manipulation of individual photons require cryogenic refrigerated devices. One decade later than the introduction of DV systems, an alternative approach to QKD was proposed [8, 9, 10]. It is named the continuous variable (CV) approach, since photon parameters assuming continuous values are used.  
Continuous variable quantum key distribution (CV-QKD) systems reuse devices already developed for classical optical communication systems and that have been commercially available for decades, such as positive-intrinsic-negative (PIN) photodiodes, reducing system complexity and cost. CV-QKD refers to a family of protocols divided in two macro subclasses, named discrete and gaussian modulation. For a complete description of the topic, interested readers can look at [11].  
We can consider CV-QKD as an adaptation of the BB84 protocol to be used with non-discrete characteristics of light. It uses well-studied homodyne detection, transmitting pulses of energy instead of single-photons. In the first proposal, squeezed optical pulses are used. Each pulse can be transmitted over one of the two quadrature components of the complex plane, adding a constant displacement to encode \"0\" or \"1\" bits. The receiver then randomly chooses the quadrature component in which to perform measurements, adopting an algorithm analogous to BB84, and keeping only the measures for which the correct quadrature choice was made. If the measure is performed on the correct plane, the result is then Gaussian-distributed with mean value equal to the applied displacement used to decode the bits. A viable alternative to the squeezed states, which are intrinsically hard to generate, is the use of coherent states in the complex plane, which are much easier to generate [12]. The idea remains similar to the exposed one; the difference is that more complex constellations of coherent states can be generated to encode information, such as in [13,14], where four and eight coherent states are used. Alternatively, a Gaussian approach can be adopted, where the displacement the sender introduces between the states follows a Gaussian distribution. The first proposal repeated using squeezed states [15], then many alternatives based on coherent states are proposed, together with practical implementations [16, 17, 18, 19].  
Discrete CV-QKD protocols (i.e., using a fixed displacement) are closer to practical implementations and also enable higher distance reach [20]. On the other hand, security features for discrete modulated CV-QKD are harder to proof than Gaussian CV-QKD. The lower the number of states, the harder it is to prove that the protocol is secure. Indeed, in discretizing the signal, finite-size statistical effects progressively become more relevant, increasing the complexity of a theoretical security proof. Many articles exist on the topic of the security of CV-QKD, and a general review is covered in [21]. It is worth to noting that while for DV-QKD many security proofs exist (including non-ideal devices), assuming unlimited computational power and memory [22], the state of the security proofs in the context of CV-QKD is more limited. For the Gaussian approach, the security is guaranteed only for infinite or unpractically long keys.  
From an industrial perspective, CV-QKD represents a promising opportunity whenever the reuse of the network infrastructure is important, as well as the integration of the QKD system with a classical network. Its early maturity level and the low number of performed tests and theoretical security proofs, together with its limits in terms of performance and complexity in performing reconciliation, make CV-QKD a longer-term solution compared to DV-QKD.