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IEEE International Symposium on Information Theory (ISIT)

Quantum Broadcast Channels with Cooperating Decoders: An Information-Theoretic Perspective on Quantum Repeaters

Uzi Pereg, Christian Deppe, Holger Boche

Published Jul 12, 2021• 7 citations
Publisher

Abstract

Communication over a quantum broadcast channel with cooperation between the receivers is considered. The first form of cooperation addressed is classical conferencing. Another cooperation setting involves quantum conferencing, where Receiver 1 can teleport a quantum state to Receiver 2. The conferencing setting is intimately related to quantum repeaters, as the sender, Receiver 1, and Receiver 2 can be viewed as the transmitter, the repeater, and the destination receiver, respectively. We develop lower and upper bounds on the capacity region in each setting. At last, we show that as opposed to the MAC with entangled encoders, entanglement between decoders does not increase the classical communication rates for the broadcast dual.

DOI
10.1109/isit45174.2021.9518284

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IEEE Transactions on Information Theory•Sep 22, 2025•3 citations
Communication over a quantum broadcast channel with cooperation between the receivers is considered. The first form of cooperation addressed is classical conferencing. Another cooperation setting involves quantum conferencing, where Receiver 1 can teleport a quantum state to Receiver 2. The conferencing setting is intimately related to quantum repeaters, as the sender, Receiver 1, and Receiver 2 can be viewed as the transmitter, the repeater, and the destination receiver, respectively. We develop lower and upper bounds on the capacity region in each setting. At last, we show that as opposed to the MAC with entangled encoders, entanglement between decoders does not increase the classical communication rates for the broadcast dual.
Communication over a quantum broadcast channel with cooperation between the receivers is considered. The first form of cooperation addressed is classical conferencing, where receiver 1 can send classical messages to receiver 2. Another cooperation setting involves quantum conferencing, where receiver 1 can teleport a quantum state to receiver 2. When receiver 1 is not required to recover information and its sole purpose is to help the transmission to receiver 2, the model reduces to the quantum primitive relay channel. The quantum conferencing setting is intimately related to quantum repeaters as the sender, receiver 1, and receiver 2 can be viewed as the transmitter, the repeater, and the destination receiver, respectively. We develop lower and upper bounds on the capacity region in each setting. In particular, the cutset upper bound and the decode-forward lower bound are derived for the primitive relay channel. Furthermore, we present an entanglement-formation lower bound, where a virtual channel is simulated through the conference link. At last, we show that as opposed to the multiple access channel with entangled encoders, entanglement between decoders does not increase the classical communication rates for the broadcast dual.
We prove coding theorems for two scenarios of cooperating encoders for the multiple access channel with two classical inputs and one quantum output. In the first scenario (ccq-MAC with common message), the two senders each have their private messages, but would also like to transmit common messages. In the second scenario (ccq-MAC with conferencing encoders), each sender has its own set of messages, but they are allowed to use a limited amount of noiseless classical communication amongst each other prior to encoding their messages. This conferencing protocol may depend on each individual message they intend to send. The two scenarios are related to each other not only in spirit - the existence of a capacity-achieving construction scheme for codes for the ccq-MAC with common messages is used for proving the existence of another such scheme for the ccq-MAC with conferencing encoders.
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 ],
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.
We consider quantum and private communications assisted by repeaters, from the basic scenario of a single repeater chain to the general case of an arbitrarily-complex quantum network, where systems may be routed through single or multiple paths. In this context, we investigate the ultimate rates at which two end-parties may transmit quantum information, distribute entanglement, or generate secret keys. These end-to-end capacities are defined by optimizing over the most general adaptive protocols that are allowed by quantum mechanics. Combining techniques from quantum information and classical network theory, we derive single-letter upper bounds for the end-to-end capacities in repeater chains and quantum networks connected by arbitrary quantum channels, establishing exact formulas under basic decoherence models, including bosonic lossy channels, quantum-limited amplifiers, dephasing and erasure channels. For the converse part, we adopt a teleportation-inspired simulation of a quantum network which leads to upper bounds in terms of the relative entropy of entanglement. For the lower bounds we combine point-to-point quantum protocols with classical network algorithms. Depending on the type of routing (single or multiple), optimal strategies corresponds to finding the widest path or the maximum flow in the quantum network. Our theory can also be extended to simultaneous quantum communication between multiple senders and receivers.
Communication over a fully quantum relay channel is considered. We establish three bounds based on different coding strategies, i.e., partial decode-forward, measure-forward, and assist-forward. Using the partial decode-forward strategy, the relay decodes part of the information, while the other part is decoded without the relay’s help. The result by Savov et al. (2012) for a classical-quantum relay channel is obtained as a special case. Based on our partial decode-forward bound, the capacity is determined for Hadamard relay channels. In the measure-forward coding scheme, the relay performs a sequence of measurements and then sends a compressed representation of the measurement outcome to the destination receiver. The measure-forward strategy can be viewed as a generalization of the classical compress-forward bound. At last, we consider quantum relay channels with orthogonal receiver components. The assist-forward bound is based on a new approach, whereby the transmitter sends the message to the relay and simultaneously generates entanglement assistance between the relay and the destination receiver. Subsequently, the relay can transmit the message to the destination receiver with rate-limited entanglement assistance.