Multicasting Homogeneous and Heterogeneous Quantum States in Quantum Networks

TL;DR

This paper presents recursive lossless compression methods for quantum multicast networks, enabling efficient transmission of homogeneous and heterogeneous quantum states while analyzing the trade-offs and bandwidth requirements.

Contribution

It introduces novel recursive lossless compression schemes for quantum states, applicable to various network topologies, addressing practical implementation challenges in quantum multicast networks.

Findings

Recursive compression controls circuit complexity and state dimension.

Heterogeneous schemes outperform homogeneous compression in certain structures.

Bandwidth analysis for different quantum network models.

Abstract

In this paper, we target the practical implementation issues of quantum multicast networks. First, we design a recursive lossless compression that allows us to control the trade-off between the circuit complexity and the dimension of the compressed quantum state. We give a formula that describes the trade-off, and further analyze how the formula is affected by the controlling parameter of the recursive procedure. Our recursive lossless compression can be applied in a quantum multicast network where the source outputs homogeneous quantum states (many copies of a quantum state) to a set of destinations through a bottleneck. Such a recursive lossless compression is extremely useful in the current situation where the technology of producing large-scale quantum circuits is limited. Second, we develop two lossless compression schemes that work for heterogeneous quantum states (many copies of a set of quantum states) when the set of quantum states satisfies a certain structure. The heterogeneous compression schemes provide extra compressing power over the homogeneous compression scheme. Finally, we realize our heterogeneous compression schemes in several quantum multicast networks, including the single-source multi-terminal model, the multi-source multi-terminal model, and the ring networks. We then analyze the bandwidth requirements for these network models.