Entanglement-assisted capacity regions and protocol designs for quantum multiple-access channels

Abstract

We solve the entanglement-assisted (EA) classical capacity region of quantum multiple-access channels (MACs) with an arbitrary number of senders. As an example, we consider the bosonic thermal-loss MAC and solve the one-shot capacity region enabled by an entanglement source composed of sender-receiver pairwise two-mode squeezed vacuum states. The EA capacity region is strictly larger than the capacity region without entanglement-assistance. With two-mode squeezed vacuum states as the source and phase modulation as the encoding, we also design practical receiver protocols to realize the entanglement advantages. Four practical receiver designs, based on optical parametric amplifiers, are given and analyzed. In the parameter region of a large noise background, the receivers can enable a simultaneous rate advantage of 82.0% for each sender. Due to teleportation and superdense coding, our results for EA classical communication can be directly extended to EA quantum communication at half of the rates. Our work provides a unique and practical network communication scenario where entanglement can be beneficial.

Computable limits of optical multiple-access communications

“…, R s ) is said to be achievable if the (average) error rate of decoding is suppressed arbitrarily small when the code word length is sufficiently large (for a formal definition, see Refs. [26,28,29]). These rates in general have non-trivial trade-offs with each other, thus their collection forms a non-trivial region in the s-dimensional vector space.…”

“…In Ref. [29], the rate-region of the common entanglement source TMSV has been evaluated for a thermal-loss MAC, which provides an achievable rate region. However, the exact capacity is unknown due to the difficulty brought by: (a) the regularization in Eq.…”

“…Therefore, interference BGMACs form a fairly general class of BGMACs. Indeed, interference-BGMACs are relevant in applications, and all of the BGMACs considered in the literature are in this class [29][30][31][32]. Formally, the interference BGMAC N is a concatenation…”

“…We prove so via extending the additivity of total rate known for the two-sender case [28] to the general case. While the sum rate provides an outer bound of the EA capacity region, the Gaussian optimality in total rate inspires us to examine the Gaussianstate capacity region of a class of interference BGMACs, which is practically relevant and includes all BGMACs considered in the literature [29][30][31][32]. With two or three senders, we numerically find that two-mode squeezed vacuum (TMSV) states to be the optimal Gaussian entanglement.…”

“…The classical capacity region of a general broadcast channel is still an open problem with or without EA [16,17], except for special cases [16,[18][19][20]. For bosonic optical broadcast channels, although the capacity formula is known in the pure-loss case [19,20], the classical capacity region is still subject to the multi-mode 'entropy photon number inequality' conjecture [21][22][23][24]; for phase-insensitive bosonic Gaussian MACs (BGMACs) that model optical networks, the classical capacity formula with and without EA are known [25][26][27][28][29], but their evaluation is still an open question as the additivity of them is unknown [29,30]. Indeed, unlike the singlesender and single-receiver case, the problem of additivity is complicated by the trade-off between the different senders.…”