Schemes of transmission of classical information via quantum channels with many senders: discrete and continuous variables cases

TL;DR

This paper investigates superadditivity effects in the classical capacity of quantum multiple access channels for both discrete and continuous variables, providing new examples, analyzing entanglement requirements, and exploring noise sensitivity.

Contribution

It introduces new instances of superadditivity, demonstrates the necessity of multi-copy entanglement, and refines understanding of capacity enhancement in CV channels.

Findings

Superadditivity observed in symmetric discrete channels.

Multi-copy entanglement surpasses two-copy limits.

Capacity superadditivity is more robust to thermal noise than previously thought.

Abstract

Superadditivity effects in the classical capacity of discrete multi-access channels (MACs) and continuous variable (CV) Gaussian MACs are analysed. New examples of the manifestation of superadditivity in the discrete case are provided including, in particular, a channel which is fully symmetric with respect to all senders. Furthermore, we consider a class of channels for which {\it input entanglement across more than two copies of the channels is necessary} to saturate the asymptotic rate of transmission from one of the senders to the receiver. The 5-input entanglement of Shor error correction codewords surpass the capacity attainable by using arbitrary two-input entanglement for these channels. In the CV case, we consider the properties of the two channels (a beam-splitter channel and a "non-demolition" XP gate channel) analyzed in [Czekaj {\it et al.}, Phys. Rev. A {\bf 82}, 020302 (R) (2010)] in greater detail and also consider the sensitivity of capacity superadditivity effects to thermal noise. We observe that the estimates of amount of two-mode squeezing required to achieve capacity superadditivity are more optimistic than previously reported.