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Journal of Nanjing University of Posts and Telecommunications

Proof of Capacity Theorem of Noisy Multiple Access Quantum Channels and Its Application

Shengmei Zhao

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

Research on capacity of noisy multiple access quantum channels is the basis of the quantum multi-user communications.According to the classical-quantum entanglement generation theorem and the quantum-quantum entanglement generation theorem,the capacity regions,comprised classical-quantum region and quantum-quantum region,and noisy multiple access quantum channels are deduced in this paper.Then,the theorem is applied to the computation of quantum-quantum capacity region of the multiple access phase-flip channel,and the result The result verifies the theorem,and the quantum-quantum capacity region turns out to be a pentagonal region.For simplicity and generality,we consider the multiple access quantum channels with two senders and one receiver.

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Research on capacity of noisy multiple access quantum channels is the basis of the quantum multi-user communications.According to the classical-quantum entanglement generation theorem and the quantum-quantum entanglement generation theorem,the capacity regions,comprised classical-quantum region and quantum-quantum region,and noisy multiple access quantum channels are deduced in this paper.Then,the theorem is applied to the computation of quantum-quantum capacity region of the multiple access phase-flip channel,and the result The result verifies the theorem,and the quantum-quantum capacity region turns out to be a pentagonal region.For simplicity and generality,we consider the multiple access quantum channels with two senders and one receiver.
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Quantum broadcast channels are the fundamental of quantum network communication.To use the channel efficiently and effectively,it is crucial to know the capacity region of the channel.In this paper,we focus on the capacity region problem of quantum broadcast channel with only one sender and two receivers.According to the quantum entanglement generation theorem,we present and prove the capacity theorems of noisy quantum broadcast channels,including classical-quantum and quantum-quantum capacity region theorems,by which we obtain the capacity region of the quantum broadcast channel with depolarizing noise.
We consider quantum channels with two senders and one receiver. For an arbitrary such channel, we give multiletter characterizations of two different two-dimensional capacity regions. The first region comprises the rates at which it is possible for one sender to send classical information, while the other sends quantum information. The second region consists of the rates at which each sender can send quantum information. For each region, we give an example of a channel for which the corresponding region has a single-letter description. One of our examples relies on a new result proved here, perhaps of independent interest, stating that the coherent information over any degradable channel is concave in the input density operator. We conclude with connections to other work and a discussion on generalizations where each user simultaneously sends classical and quantum information.
We consider quantum channels with two senders and one receiver. For an arbitrary such channel, we give multi-letter characterizations of two different two-dimensional capacity regions. The first region characterizes the rates at which it is possible for one sender to send classical information while the other sends quantum information. The second region gives the rates at which each sender can send quantum information. We give an example of a channel for which each region has a single-letter description, concluding with a characterization of the rates at which each user can simultaneously send classical and quantum information
The depolarizing channel is one of the basic quantum channels.For simplicity and generality, quantum channels with two senders and one receiver are considered to discuss the capacity of the quantum depolarizing channel.Two different capacity regions,classical-quantum region and quantum-quantum re- gion,are deduced in theory for the quantum depolarizing channels with two senders and one receiver.The first region is comprised of the rates at which it is achievable for one sender to transmit classical information, while the other to send quantum information.The other region consists of the rates at which each sender sends quantum information.At the same time,the performance of the quantum multiple access depolarizing channel is analyzed.
We find a regularized formula for the entanglement-assisted (EA) capacity region for quantum multiple-access channels (QMAC). We illustrate the capacity region calculation with the example of the collective phase-flip channel which admits a single-letter characterization. On the way, we provide a first-principles proof of the EA coding theorem based on a packing argument. We observe that the Holevo-Schumacher-Westmoreland theorem may be obtained from a modification of our EA protocol. We remark on the existence of a family hierarchy of protocols for multiparty scenarios with a single receiver, in analogy to the two-party case. In this way, we relate several previous results regarding QMACs.