Path selection for quantum repeater networks

Abstract

Quantum networks will support long-distance quantum key distribution (QKD) and distributed quantum computation, and are an active area of both experimental and theoretical research. Here, we present an analysis of topologically complex networks of quantum repeaters composed of heterogeneous links. Quantum networks have fundamental behavioral differences from classical networks; the delicacy of quantum states makes a practical path selection algorithm imperative, but classical notions of resource utilization are not directly applicable, rendering known path selection mechanisms inadequate. To adapt Dijkstra's algorithm for quantum repeater networks that generate entangled Bell pairs, we quantify the key differences and define a link cost metric, seconds per Bell pair of a particular fidelity, where a single Bell pair is the resource consumed to perform one quantum teleportation. Simulations that include both the physical interactions and the extensive classical messaging confirm that Dijkstra's algorithm works well in a quantum context. Simulating about three hundred heterogeneous paths, comparing our path cost and the total work along the path gives a coefficient of determination of 0.88 or better.

Entanglement accessibility measures for the quantum Internet

“…since the entanglement swapping (extension) procedure doubles the span of the entangled pair in each step. This architecture is also referred to as the doubling architecture [15,[24][25][26]. For a particular L l -level entangled connection E L l (x, y) with hop-distance (2), there are d (x, y) L l − 1 intermediate nodes between the quantum nodes x and y.…”

“…where F in is the fidelity of the imperfect input Bell pairs. The purification requires the use of two-way classical communications [12,15,[22][23][24][25][26]29]. Let B F (E i L l ) refer to the entanglement throughput of a given L l entangled connection E i L l measured in the number of d-dimensional entangled states established over E i L l per sec at a particular fidelity F (dimension of a qubit system is d = 2) [12,15,[22][23][24][25][26]29].…”

“…As an important corollary, an entangled network structure provides a strong experimental basis for realizing a global-scale quantum communication network, the quantum Internet.In the entangled network structure of the quantum Internet, the entangled connections form entangled paths. Entanglement between a distant source and a target node is established through several intermediate repeater nodes [15,18,[24][25][26]. The level of entanglement (i.e., the level of an entangled connection) is defined as the number of nodes (i.e., the hop-distance between entangled nodes) spanned by the shared entanglement, whose range is extended by the basic operation of entanglement swapping (entanglement extension).…”

Theory of Noise-Scaled Stability Bounds and Entanglement Rate Maximization in the Quantum Internet

“…since the entanglement swapping (extension) procedure doubles the span of the entangled pair in each step. This architecture is also referred to as the doubling architecture [10,[14][15][16].…”

Secret key rates of free‐space optical continuous‐variable quantum key distribution

“…Free‐space optical (FSO) quantum links provide a tool to implement quantum communications via wireless telecommunication network infrastructures. As an integrated component of future quantum Internet and long‐distance quantum communications, the FSO quantum channels could play a significant role in the global‐scale practical implementations of quantum communications and quantum key distribution (QKD) . QKD systems allow us to utilize the fundamentals of quantum mechanics to realize unconditionally secure communications for legal users.…”