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arXiv:1209.0120 · Open Systems & Information Dynamics

Decoherence-Free Communication over Multiaccess Quantum Channels

Maciej Demianowicz

Published Jun 1, 2013• 1 citation
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Abstract

In this paper we consider decoherence-free communication over multiple access and k-user quantum channels. First, we concentrate on a hermitian unitary noise model U for a two-access bi-unitary channel and show that in this case a decoherence-free code exists if the space of Schmidt matrices of an eigensubspace of U exhibits certain properties of decomposability. Then, we show that our technique is also applicable for generic random unitary two-access channels. Finally, we consider the applicability of the result to the case of a larger number of senders and general Kraus operators.

DOI
10.1142/s1230161213500078

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In this paper we consider decoherence-free communication over multiple access and k-user quantum channels. First, we concentrate on a hermitian unitary noise model U for a two-access bi-unitary channel and show that in this case a decoherence-free code exists if the space of Schmidt matrices of an eigensubspace of U exhibits certain properties of decomposability. Then, we show that our technique is also applicable for generic random unitary two-access channels. Finally, we consider the applicability of the result to the case of a larger number of senders and general Kraus operators.
In this paper we consider construction of decoherence free subspaces for two--access random unitary channels. First, we concentrate on hermitian unitary noise model UUU for a bi--unitary channel and show that in this case a code exists if the space of Schmidt matrices of an eigensubspace of UUU exhibits certain properties of decomposability. Then, we show that our technique is also applicable in a generic case and consider its application two tri- (quatro-, ...) unitary channels.
Shared communication channels are subject to multiple-access interference. Transmitter and receiver design techniques that explicitly deal with this interference have been shown to improve substantially the performance of communication systems over radio-frequency and other "classical" channels. Quantum multiple-access communication channels, on the other hand, have received comparatively little attention. In this paper, an input-output model for multiple-access quantum channels relevant to optical communications is proposed. The model accounts for multiaccess interference, signal attenuation, and random noise, and can be used in the analysis and design of communication systems. Using a result from optimization, a perturbation method is developed to find the minimum achievable error probability in small-interference channels. It is shown that the quantum measurement that minimizes the error probability in a no-interference channel is robust in the presence of small multiaccess interference. The results are illustrated with numerical examples, which show that optimal quantum detectors can significantly outperform conventional detectors even for moderate levels of crosstalk.
All free-space quantum communications require the use of a quantum channel, which transports quantum bits in such a way that the quantum mechanical states of the qubits remain preserved from one end of the channel to the other one. In quantum computing the classical error coding methods could not be used, however we can construct a classical channel with zero redundancy error correction for any unitary channel. In our basically new quantum error correction approach, the classical states are coded into the eigenvectors and unitary transformations. In this paper, we show that with our new algorithm it’s possible to create redundancy-free quantum error correction. We also consider the redundancy-free implementation of a unitary error correcting operator. Our protocol achieves the redundancy-free quantum communication using local unitary operations and unitary matrices. These solutions could be useful for the free-space quantum communication.
In communication networks many different channels must share a limited amount of resources. In order to allow for multiple simultaneous communications, multiple access techniques are routinely employed. With quantum communication, it is possible to share a new kind of resource. All of the system channels can be accommodated into a single channel in a larger Hilbert space. In the scheme, a single line combines the information of all the users, and, at the receiver, the original quantum channels are recovered. The given multiplexer/demultiplexer circuit can perform this n qubits to qudit transformation. Connections with superdense coding and classical multiple access schemes are discussed.
The discrete memoryless interference channel is modelled as a conditional probability distribution with two outputs depending on two inputs and has widespread applications in practical communication scenarios. In this paper, we introduce and study the quantum interference channel, a generalization of a two-input, two-output memoryless channel to the setting of quantum Shannon theory. We discuss three different coding strategies and obtain corresponding achievable rate regions for quantum interference channels. We calculate the capacity regions in the special cases of "very strong" and "strong" interference. The achievability proof in the case of "strong" interference exploits a novel quantum simultaneous decoder for two-sender quantum multiple access channels. We formulate a conjecture regarding the existence of a quantum simultaneous decoder in the three-sender case and use it to state the rates achievable by a quantum Han-Kobayashi strategy.
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.