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首页> 外文期刊>Information Theory, IEEE Transactions on >Quantum Network Communication—The Butterfly and Beyond
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Quantum Network Communication—The Butterfly and Beyond

机译：量子网络通信—蝴蝶与超越

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摘要

We study the problem of $k$-pair communication (or multiple unicast problem) of quantum information in networks of quantum channels. We consider the asymptotic rates of high fidelity quantum communication between specific sender-receiver pairs. Four scenarios of classical communication assistance (none, forward, backward, and two-way) are considered. (I) We obtain outer and inner bounds of the achievable rate regions in the most general directed networks. (II) For two particular networks (including the butterfly network), routing is proved optimal, and the free assisting classical communication can at best be used to modify the directions of quantum channels in the network. Consequently, the achievable rate regions are given by counting edge avoiding paths, and precise achievable rate regions in all four assisting scenarios can be obtained. (III) Optimality of routing can also be proved in classes of networks. The first class consists of directed unassisted networks in which (1) the receivers are information sinks, (2) the maximum distance from senders to receivers is small, and (3) a certain type of 4-cycles are absent, but without further constraints (such as on the number of communicating and intermediate parties). The second class consists of arbitrary backward-assisted networks with two sender-receiver pairs. (IV) Beyond the $k$-pair communication problem, observations are made on quantum multicasting and a static version of network communication related to the entanglement of assistance.
机译：我们研究了量子信道网络中量子信息的$ k $对通信问题（或多个单播问题）。我们考虑特定发送方-接收方对之间高保真量子通信的渐近速率。考虑了经典通信协助的四种情况（无，前进，后退和双向）。 （I）我们在最普通的有向网络中获得了可达到的汇率区域的外边界和内边界。 （II）对于两个特定的网络（包括蝶形网络），路由被证明是最优的，并且免费辅助经典通信最多可以用来修改网络中量子信道的方向。因此，通过对边缘避开路径进行计数来给出可达到的速率区域，并且可以在所有四种辅助情况下获得精确的可达到的速率区域。 （III）路由的最优性也可以在网络类别中得到证明。第一类由定向无辅助网络组成，其中（1）接收者是信息接收器；（2）从发送者到接收者的最大距离很小；（3）缺少某种类型的4周期，但没有进一步的限制（例如，交流方和中介方的数量）。第二类由具有两个发送者-接收者对的任意后向辅助网络组成。 （IV）除了$ k $对通信问题之外，还观察到量子多播和与协助纠缠有关的网络通信的静态版本。

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