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IEEE International Symposium on Information Theory (ISIT)

Entanglement-assisted multiple-access channels: capacity regions and protocol designs

Haowei Shi, Min-Hsiu Hsieh, Saikat Guha, Zheshen Zhang, Quntao Zhuang

Published Jan 1, 2021• 4 citations
Publisher

Abstract

We solve the entanglement-assisted (EA) classical capacity region of quantum multiple-access channels with an arbitrary number of senders, which is conjectured by Hsieh, Devetak and Winter. As an example, we consider the bosonic thermal-loss multiple-access channel and solve the rate region enabled by an entanglement source composed of sender-receiver pairwise two-mode squeezed vacuum states. The EA rate region is strictly larger than the capacity region without entanglement-assistance, therefore also larger than the Yen-Shapiro rate-region of Gaussian encoding or coherent-state encoding. When the senders have equal low brightness, we also numerically find that the two-mode squeezed vacuum source is optimal at a corner rate point. 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. In the parameter region of a large noise background, the receivers can enable a simultaneous rate advantage of 82.0% for each sender with binary phase-shift keying. 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.

DOI
10.1109/isit45174.2021.9518082

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We solve the entanglement-assisted (EA) classical capacity region of quantum multiple-access channels with an arbitrary number of senders, which is conjectured by Hsieh, Devetak and Winter. As an example, we consider the bosonic thermal-loss multiple-access channel and solve the rate region enabled by an entanglement source composed of sender-receiver pairwise two-mode squeezed vacuum states. The EA rate region is strictly larger than the capacity region without entanglement-assistance, therefore also larger than the Yen-Shapiro rate-region of Gaussian encoding or coherent-state encoding. When the senders have equal low brightness, we also numerically find that the two-mode squeezed vacuum source is optimal at a corner rate point. 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. In the parameter region of a large noise background, the receivers can enable a simultaneous rate advantage of 82.0% for each sender with binary phase-shift keying. 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.
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.
Entanglement is a valuable quantum resource in quantum information processing. In classical communication over quantum channels, it is known to boost the communication rate drastically. To generalize such a boost to more general scenarios, we provide computable limits on the communication over optical multiple-access channels (MACs) for both the entanglement-assisted and unassisted communication. For the unassisted case, we generalize the coherent-state achievable rate region and outer bound known for the thermal-loss case [B. J. Yen and J. H. Shapiro, Phys. Rev. A 72, 062312 (2005)] to general bosonic Gaussian MACs. For the assisted case, we generalize the two-mode squeezed vacuum rate region and the outer bound for the thermal-loss case [H. Shi et al., npj Quantum Inf. 7, 74 (2021)] to general bosonic MACs. In terms of the total communication rate of all senders, we prove additivity for general MACs, generalizing the two-sender version in M.-H. Hsieh et al., IEEE Trans. Inf. Theory 54, 3078 (2008). Furthermore, for optical communication modeled as phase-insensitive bosonic Gaussian MACs, we prove that the optimal total rate is achieved by Gaussian entanglement and therefore can be efficiently evaluated. The computable limits confirm entanglement's boosts in optical multiple-access communications. Finally, we formulate an entanglement-assisted version of minimum entropy conjecture, which leads to the additivity of the capacity region of phase-insensitive bosonic Gaussian MACs if it is true.
We consider the problem of covert communication over the entanglement-assisted (EA) bosonic multiple access channel (MAC). We derive a closed-form achievable rate region for the general EA bosonic MAC using high-order phase-shift keying (PSK) modulation. Specifically, we demonstrate that in the low-photon regime the capacity region collapses into a rectangle, asymptotically matching the point-to-point capacity as multi-user interference vanishes. We also characterize an achievable covert throughput region, showing that entanglement assistance enables an aggregate throughput scaling of O(nlog⁡n)O(\sqrt{n} \log n)O(n​logn) covert bits with the block length nnn for both senders, surpassing the square-root law as in the point-to-point case. Our analysis reveals that the joint covertness constraint imposes a linear trade-off between the senders throughput.
Communication over a multiple-access channel (MAC) with entanglement assisted and conferencing transmitters is considered, where the transmitters can also communicate with each other over rate-limited links. We fully characterize the capacity region for the MAC with entangled transmitters and classical conferencing. We also introduce a quantum conferencing protocol. For the MAC with entangled transmitters and quantum conferencing, we determine a achievable region. This region is generally larger than the capacity region for the MAC with entangled transmitters and classical conferencing. Using superdense coding, entanglement can double the conferencing rate. We continue to discuss potential applications of cooperation between the transmitters for the future 6G system. This is only a short abstract. The long version with all proofs can be found on arxiv [l ],
Entanglement offers substantial advantages in quantum information processing, but loss and noise hinder its application in practical scenarios. Although it has been well known for decades that the classical communication capacity of lossy and noisy bosonic channels can be significantly enhanced by entanglement, no practical encoding and decoding schemes are available to realize any entanglement-enabled advantage. Here, we report structured encoding and decoding schemes for such an entanglement-assisted communication scenario. Specifically, we show that phase encoding on an entangled two-mode squeezed vacuum state saturates the entanglement-assisted classical communication capacity of a very noisy channel and overcomes the fundamental limit on covert communication that exists without the assistance of entanglement. We then construct receivers for optimum hypothesis-testing protocols with discrete phase modulation and for optimum noisy phase-estimation protocols with continuous phase modulation. Our results pave the way for entanglement-assisted communication and sensing in the radio-frequency and microwave spectral ranges.
Abstract We consider entanglement-assisted (EA) private communication over a quantum broadcast channel, in which there is a single sender and multiple receivers. We divide the receivers into two sets: the decoding set and the malicious set. The decoding set and the malicious set can either be disjoint or can have a finite intersection. For simplicity, we say that a single party Bob has access to the decoding set and another party Eve has access to the malicious set, and both Eve and Bob have access to the pre-shared entanglement with Alice. The goal of the task is for Alice to communicate classical information reliably to Bob and securely against Eve, and Bob can take advantage of pre-shared entanglement with Alice. In this framework, we establish a lower bound on the one-shot EA private capacity. When there exists a quantum channel mapping the state of the decoding set to the state of the malicious set, such a broadcast channel is said to be degraded. We establish an upper bound on the one-shot EA private capacity in terms of smoothed min- and max-entropies for such channels. In the limit of a large number of independent channel uses, we prove that the EA private capacity of a degraded quantum broadcast channel is given by a single-letter formula. Finally, we consider two specific examples of degraded broadcast channels and find their capacities. In the first example, we consider the scenario in which one part of Bob’s laboratory is compromised by Eve. We show that the capacity for this protocol is given by the conditional quantum mutual information of a quantum broadcast channel, and so we thus provide an operational interpretation to the dynamic counterpart of the conditional quantum mutual information. In the second example, Eve and Bob have access to mutually exclusive sets of outputs of a broadcast channel.