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Chinese Journal of Quantum Electronics

Capacity of the quantum multiple access depolarizing channel

Shengmei Zhao

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

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.

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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 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 rates at which classical and quantum information can be simultaneously transmitted from two spatially separated senders to a single receiver over an arbitrary quantum channel are characterized. Two main results are proved in detail. The first describes the region of rates at which one sender can send classical information while the other sends quantum information. The second describes those rates at which both senders can send quantum information. For each of these situations, an example of a channel is given for which the associated region admits a single-letter description. This is the author's Ph.D. dissertation, submitted to the Department of Electrical Engineering at Stanford University in March, 2005. It represents an expanded version of the paper quant-ph/0501045, containing a number of tutorial chapters which may be of independent interest for those learning about quantum Shannon theory.
As its classical counterpart，quantum Gaussian noise is an important noise model in quantum information theory. The study of capacity of quantum Gaussian channel plays an important role in quantum communications. Based on the definition of quantum Gaussian state，the entropy of quantum Gaussian state，and Holevo bound theorem，the classical capacity of quantum Gaussian channel is given at first in the paper，where the classical capacity is defined as the capacity when only classical messages are transmitted through the quantum channel. Then，the classical capacities of quantum multiple access Gaussian channels are deduced according to the classical capacity theorem of multiple access quantum channels. For simplicity and generality，a multiple access quantum channel with two senders and one receiver is used for computation. The results can be generalized to the quantum channel with n senders and one receiver.
We analyze the quantum binary adder channel, i.e. the quantum generalization of the classical, and well-studied, binary adder channel: in this model qubits rather than classical bits are transmitted. This of course is as special case of the general theory of quantum multiple access channels, and we may apply the established formulas for the capacity region to it. However, the binary adder channel is of particular interest classically, which motivates our generalizing it to the quantum domain. It turns out to be a very nice case study not only of multi-user quantum information theory, but also on the role entanglement plays there. It turns out that the analogous classical situation, the multi-user channel supported by shared randomness, is not distinct from the channel without shared randomness, as far as rates are concerned. However, we discuss the effect the new resource has on error probabilities, in an appendix. We focus specially on the effect entanglement between the senders as well as between senders and receiver has on the capacity region. Interestingly, in some of these cases one can devise rather simple codes meeting the capacity bounds, even in a zero-error model, which is in marked difference to code construction in the classical case.
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.