Capacities of repeater-assisted quantum communications

TL;DR

This paper establishes fundamental limits on quantum communication capacities in repeater-assisted networks, providing exact formulas and bounds for various channel models and routing strategies, advancing understanding of quantum network performance.

Contribution

It introduces single-letter upper bounds and exact formulas for quantum network capacities, integrating quantum information theory with classical network algorithms.

Findings

Derived upper bounds for end-to-end capacities in quantum networks.

Established exact capacity formulas for basic decoherence models.

Linked optimal routing strategies to classical network algorithms like maximum flow.

Abstract

We consider quantum and private communications assisted by repeaters, from the basic scenario of a single repeater chain to the general case of an arbitrarily-complex quantum network, where systems may be routed through single or multiple paths. In this context, we investigate the ultimate rates at which two end-parties may transmit quantum information, distribute entanglement, or generate secret keys. These end-to-end capacities are defined by optimizing over the most general adaptive protocols that are allowed by quantum mechanics. Combining techniques from quantum information and classical network theory, we derive single-letter upper bounds for the end-to-end capacities in repeater chains and quantum networks connected by arbitrary quantum channels, establishing exact formulas under basic decoherence models, including bosonic lossy channels, quantum-limited amplifiers, dephasing and erasure channels. For the converse part, we adopt a teleportation-inspired simulation of a quantum network which leads to upper bounds in terms of the relative entropy of entanglement. For the lower bounds we combine point-to-point quantum protocols with classical network algorithms. Depending on the type of routing (single or multiple), optimal strategies corresponds to finding the widest path or the maximum flow in the quantum network. Our theory can also be extended to simultaneous quantum communication between multiple senders and receivers.