# Bounds for multi-end communication over quantum networks

## TL;DR

This paper establishes fundamental bounds on the maximum achievable rates for multi-end quantum communication networks, encompassing various configurations like unicast, multicast, and multiple-multicast, regardless of protocol adaptiveness.

## Contribution

It introduces universal bounds for quantum network communication rates in complex multi-end scenarios, extending beyond simple unicast settings.

## Key findings

- Bounds apply to quantum information transmission, entanglement distribution, and secret key generation.
- These bounds hold for arbitrary quantum channels and adaptive protocols.
- The results unify and extend previous rate limitations in quantum network theory.

## Abstract

Quantum and private communications are affected by a fundamental limitation which severely restricts the optimal rates that are achievable by two distant parties. To overcome this problem, one needs to introduce quantum repeaters and, more generally, quantum communication networks. Within a quantum network, other problems and features may appear when we move from the basic unicast setting of single-sender/single-receiver to more complex multi-end scenarios, where multiple senders and multiple receivers simultaneously use the network to communicate. Assuming various configurations, including multiple-unicast, multicast, and multiple-multicast communication, we bound the optimal rates for transmitting quantum information, distributing entanglement, or generating secret keys in quantum networks connected by arbitrary quantum channels. These bounds cannot be surpassed by the most general adaptive protocols of quantum network communication.