We define metrics and measures to characterize the ratio of accessible quantum entanglement for complex network failures in the quantum Internet. A complex network failure models a situation in the quantum Internet in which a set of quantum nodes and a set of entangled connections become unavailable. A complex failure can cover a quantum memory failure, a physical link failure, an eavesdropping activity, or any other random physical failure scenario. Here, we define the terms entanglement accessibility ratio, cumulative probability of entanglement accessibility ratio, probabilistic reduction of entanglement accessibility ratio, domain entanglement accessibility ratio, and occurrence coefficient. The proposed methods can be applied to an arbitrary topology quantum network to extract relevant statistics and to handle the quantum network failure scenarios in the quantum Internet.
IntroductionAs quantum computers evolves significantly [1-10], there arises a fundamental need for a communication network that provides unconditionally secure communication and all the network functions of the traditional internet. This network structure is the quantum Internet [11][12][13][14][15]22]. The availability of quantum entanglement is a crucial aspect in any global-scale quantum Internet. The quantum Internet refers to a set of connected heterogeneous quantum communication networks realized by quantum nodes and channels (such as optical fibers or wireless optical quantum channels in the physical layer) [16,[59][60][61][62][63][64]. The quantum Internet also integrates a set of classical auxiliary communication channels to transmit auxiliary classical side-information between the quantum nodes. The quantum Internet is modeled as a global-scale quantum communication network composed of quantum subnetworks and networking components. The core network of the quantum Internet is assumed to be an entangled network structure [15,20,21,24,25,27,28,[39][40][41][42][43][44][45][46][47], which is a communication network in which the quantum nodes are connected by entangled connections. An entangled connection refers to a shared entangled system (i.e., a Bell state for qubit systems to connect two quantum nodes) between the quantum nodes. In an unentangled network structure, the quantum nodes are not necessarily connected by entanglement [16,78], and the communication between the nodes is realized in a point-to-point setting. This setting does not allow quantum communication over arbitrary distances, and an unentangled network structure can mostly be used for establishing a point-to-point quantum key distribution (QKD) [70,103] between the quantum nodes. These short distances can be extended to longer distances by the utilization of free-space quantum channels [15,70]. However, this solution is auxiliary, since it can be used only at some specific points of the unentangled network structure. Therefore, it does not represent an adequate and fundamental answer to the problem of long-distance quantum communication. Consequently, in an unentangl...