Capacity of Classical Summation over a Quantum Multiple Access Channel with Arbitrary Data and Entanglement Distributions

Core Concepts

The capacity of the Σ-QMAC, which involves classical data streams distributed across servers and quantum systems distributed among the servers, is characterized for arbitrary data replication and entanglement distribution maps. The capacity depends on both the data replication and entanglement distribution, and can require genuine multiparty entanglement to achieve.

Abstract

The paper introduces the Σ-QMAC problem, which involves S servers, K classical data streams, and T independent quantum systems. The data stream Wk is replicated at a subset of servers W(k), and the quantum system Qt is distributed among a subset of servers E(t). The servers manipulate their quantum subsystems according to their data and send them to a receiver, who must recover the sum of all data streams from the measurements.
The key results are:

The capacity of the Σ-QMAC is characterized explicitly in Theorem 1. The capacity depends on both the data replication map W and the entanglement distribution map E.

For the symmetric setting with K =
S
α
data streams, each replicated among a distinct α-subset of servers, and T =
S
β
quantum systems, each distributed among a distinct β-subset of servers, the capacity is given in Corollary 4.

Bipartite (2-party) entanglement is in general insufficient to achieve the maximal distributed superdense coding (DSC) gain in the Σ-QMAC. Multiparty entanglement is necessary in general (Corollary 3).

If each data stream is only available to a unique server, then bipartite entanglement suffices to achieve the maximal DSC gain (Corollary 6).

3-party entanglement is never necessary to achieve the capacity of the Σ-QMAC. Any 3-party entanglement can be replaced by 2-party entanglements without changing the capacity (Corollary 7).

For every S ≠ 3, there exists a Σ-QMAC setting with S servers where S-party entanglement is necessary to achieve the maximal DSC gain (Corollary 8).

Stats

The capacity of the Σ-QMAC depends on the data replication map W and the entanglement distribution map E.

Quotes

"Entanglement is arguably the most counter-intuitive aspect of quantum systems. Quantum entanglement enables correlations that are classically impossible."
"Understanding the fundamental limits of quantum entanglement phenomena is therefore essential to gauge the potential of the much-anticipated quantum internet of the future."

Key Insights Distilled From

The Capacity of Classical Summation over a Quantum MAC with Arbitrarily Distributed Inputs and Entanglements

by Yuhang Yao,S... at arxiv.org 05-07-2024

https://arxiv.org/pdf/2305.03122.pdf

Deeper Inquiries

How can the insights from the Σ-QMAC setting be extended to more general linear computation tasks over quantum networks

The insights gained from the Σ-QMAC setting can be extended to more general linear computation tasks over quantum networks by leveraging the understanding of the role of entanglement in enhancing communication efficiency. In the Σ-QMAC setting, it was established that genuine multiparty entanglement is necessary to achieve the maximal distributed superdense coding gain. This insight can be applied to design quantum network protocols for more general linear computation tasks. By incorporating multiparty entanglement strategies, quantum networks can potentially achieve higher efficiency and computational power in tasks beyond simple summation, such as matrix operations, distributed optimization, and other linear computations. Understanding the fundamental limits of entanglement in these scenarios can lead to the development of more efficient and secure quantum network protocols for a wide range of applications.

What are the implications of the necessity of genuine multiparty entanglement for achieving the maximal distributed superdense coding gain in the Σ-QMAC setting

The necessity of genuine multiparty entanglement for achieving the maximal distributed superdense coding gain in the Σ-QMAC setting has significant implications for practical quantum network design. By understanding the specific entanglement requirements for optimal performance in distributed computation tasks, quantum network designers can tailor their protocols to leverage multiparty entanglement effectively. This can lead to the development of more efficient and secure quantum communication protocols that exploit the power of entanglement for enhanced computational capabilities. Additionally, the insights from the Σ-QMAC setting can guide the design of quantum networks for applications such as secure communication, distributed computing, and quantum sensing, where multiparty entanglement plays a crucial role in achieving optimal performance.

How can this be leveraged in practical quantum network design

The capacity analysis techniques developed for the Σ-QMAC can be applied to study the fundamental limits of quantum metrology protocols involving distributed sensing and parameter estimation. By adapting the capacity analysis framework to the context of quantum metrology, researchers can investigate the role of entanglement in enhancing measurement precision and efficiency in distributed sensing networks. The insights gained from the Σ-QMAC setting, such as the necessity of genuine multiparty entanglement for achieving optimal performance, can provide valuable guidance for designing quantum metrology protocols that leverage entanglement for improved measurement accuracy. This approach can lead to advancements in quantum sensing technologies and enable the development of more precise and reliable quantum measurement systems for various applications in quantum metrology.