# On Global Quantum Communication Networking
## 1 Introduction  
Quantum communication (QuCom) employs quantum information theory concepts, in particular the no-cloning theorem and the theorem of indistinguishability of arbitrary quantum states, to implement the distribution of keys with verifiable security, commonly referred to as quantum key distribution (QKD), where security is guaranteed by the fundamental laws of physics as opposed to unproven mathematical assumptions employed in computational security-based cryptography [1; 2; 3]. Despite the appealing features of QuComs, there are some fundamental and technical challenges that need to be addressed prior to its widespread application. For instance, both the rate and distance of QuCom are fundamentally limited by channel loss, which is specified by the rate-loss tradeoff. To overcome the rate-distance limit of discrete variable (DV)-QKD protocols, two predominant approaches have been pursued recently: (i) the development of quantum relays and (ii) the employment of trusted relays. Quantum relays require the use of long-duration quantum memories and high-fidelity entanglement distillation [4], which are not yet widely available. On the other hand, the trusted-relay methodology assumes that the relay between two users can be trusted [5]; unfortunately, this assumption is difficult to verify in practice. The measurement device independent (MDI)-QKD approach [6] was able to close the detection loopholes; however, its secret-key rate (SKR) is still bounded by \(\mathcal{O}(T)\)-dependence (with \(T\) standing for transmissivity). Recently, twin-field (TF) QKD has been proposed to overcome the rate-distance limit [7], whose SKR scales with the square-root of transmittance, which represents a promising approach to extend the transmission distance. Another key limitation of DV-QKD is the deadtime of single-photon detectors (SPDs), which limits the baud rate and consequently the SKRs. To solve for this problem, a continuous variable (CV)-QKD can beused instead [1; 8; 9; 10], which employs homodyne/heterodyne detection instead and thus does not exhibit the SPDS' deadtime limitation problem. In particular, the discrete modulation (DM)-based CV-QKD protocols offer much better reconciliation efficiency compared to that of Gaussian modulation (GM)-based CV-QKD protocols. Unfortunately, the security proofs of DM-based CV-QKD schemes for collective and coherent attacks are still incomplete. To overcome key challenges for DV-QKD, such as low SKR values and limited distance, as well as for DM-based CV-QKD, such as incompleteness of security proofs, the following approaches have been proposed in our recent papers: (1) discretized GM (DGM)-CV-QKD [11], (2) optimized CV-QKD [12], and (3) hybrid DV-CV QKD [13]. An alternative approach to QKD is post-quantum cryptography (PQC) [14]. PQC is typically referred to by various cryptographic algorithms that are thought to be secure against any quantum computer-based attack. Unfortunately, PQC is also based on unproven assumptions and some of the PQC algorithms will be broken in the future by developing more sophisticated quantum algorithms. Modern classical communication networks consist of multiple nodes connected by various types of channels, including free-space optical (FSO) links, optical fibers, ground-satellite links, wireless RF, and coaxial cables. Such a heterogeneous architecture would be equally important for QCNs, as quantum nodes may access a QCN via different kinds of channels. Indeed, quantum communications have been individually validated in free-space, optical fibers, and between a satellite and a ground station, but a combined heterogeneous QCN employing multiple types of channels remains elusive. Unlike in the point-to-point communication case, the fundamental quantum communication rate limits are not well known. Several QKD testbeds have been reported so far, including the DARPA QKD network [15], Tokyo QKD network [16], and secure communication based on quantum cryptography (SECOQC) network [17].