Quantum entanglement is a building block of the entangled quantum networks of the quantum Internet. A fundamental problem of the quantum Internet is entanglement distribution. since quantum entanglement will be fundamental to any future quantum networking scenarios, the distribution mechanism of quantum entanglement is a critical and emerging issue in quantum networks. Here we define the method of opportunistic entanglement distribution for the quantum Internet. The opportunistic model defines distribution sets that are aimed to select those quantum nodes for which the cost function picks up a local minimum. the cost function utilizes the error patterns of the local quantum memories and the predictability of the evolution of the entanglement fidelities. Our method provides efficient entanglement distributing with respect to the actual statuses of the local quantum memories of the node pairs. The model provides an easily-applicable, moderate-complexity solution for high-fidelity entanglement distribution in experimental quantum Internet scenarios. Quantum entanglement has a central role in the quantum Internet 1-10 , quantum networking 11-26 , and long-distance quantum key distribution 1, 19, 27, 28 . Entanglement distribution is a crucial phase for the construction of the entangled core network structure of the quantum Internet. In a quantum Internet scenario, quantum entanglement is a preliminary condition of quantum networking protocols 27, [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] . Distant quantum nodes that share no quantum entanglement must communicate with their direct neighbors to distribute entanglement. To aim of entanglement distribution is to generate entanglement between a distant source node and a target node through a chain of intermediate quantum repeater nodes [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] . The intermediate quantum repeater nodes receive the entangled states, store them in their local quantum memories 28, 58, 59 , and apply a unitary operation (called entanglement swapping [1] [2] [3] 19 ) to extend the range of quantum entanglement. Storing quantum entanglement in the quantum nodes' local quantum memories adds noise to the distribution process, since quantum memories are non-perfect devices 34,60 and the error probabilities evolve in time 1,49-54 . As the error pattern of the evolution the quantum memories is predictable, the nodes can be characterized by a given storage success probability after a given time from the start of the storage. The fidelity of entanglement 61-63 is another critical parameter for entanglement distribution. In a quantum network with a chain of repeater nodes between a source and target nodes, for all pairs of entangled nodes (e.g., for nodes that share a common entanglement) a given lower bound in the fidelity of entanglement must be satisfied, otherwise the entanglement distribution fails 1,64 . The stored entangled states have a given amount of fidelity that is determined by the transmission procedure, such as the noise of the quantum channel, etc. The evolution of a given entangled system's fidelity parameter is time-varying in quantum memory, since it evolves through time, from the beginning of storage to the actual current time. Therefore, it is necessary to consider the predictability of the evolution of both the error patterns of the nodes' local quantum memories, and the evolution of the stored quantum states' fidelity of entanglement. In our model, using these parameters, we define an appropriate cost function for the realization of entanglement distribution. Here we define the method of opportunistic entanglement distribution for the quantum Internet. The proposed scheme utilizes a cost function that accounts for the error patterns of local quantum memories and also the evolution of entanglement fidelities. The opportunistic model defines distribution sets in the entangled quantum network of the quantum Internet. A distribution set contains those quantum nodes for which our cost function Published: xx xx xxxx opeN www.nature.com/scientificreports/
In addition, REF proposed a model that provides an applicable solution using entanglement distribution method with high fidelity to be utilized in quantum Internet networks.
Opportunistic Entanglement Distribution for the Quantum Internet
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