The Platypus of the Quantum Channel Zoo
The Platypus of the Quantum Channel Zoo
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DOI：
10.1109/tit.2023.3245985
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发表时间：
2022-02
影响因子：
2.5
通讯作者：
Felix Leditzky;D. Leung;Vikesh Siddhu;Graeme Smith;J. Smolin
中科院分区：
文献类型：
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作者：
Felix Leditzky;D. Leung;Vikesh Siddhu;Graeme Smith;J. Smolin
了解量子通道及其容量的奇怪行为是量子信息论的一个关键目标。在这里，我们研究了一个非常简单、低维、单参数的量子信道族，它具有奇异的量子信息论特征。作为这个家族最简单的例子，我们关注的是一种量子比特到量子比特的信道，它是通过将简单的可降解信道和完全无用的量子比特信道混合在一起而直观地获得的。这种混合使得这个频道的容量以各种有趣的方式表现出来。例如，该信道的私有容量和经典容量是一致的，并且可以显式地计算，即使该信道不属于任何已知其基础信息量是可加的类别。此外，如果一个清晰而令人信服的猜想是正确的，则可以显式地计算出该信道的量子容量。在某些特殊情况下证明了这一可能具有独立意义的“自旋排列猜想”，并为其正确性提供了额外的数值证据。最后，我们用两种方式推广了Qutrit通道，得到的通道及其容量表现出类似的丰富行为。在另一篇文章中，我们进一步证明了量子通道在与各种辅助通道以一种未知的方式联合传输量子信息时表现出超可加性。
Understanding quantum channels and the strange behavior of their capacities is a key objective of quantum information theory. Here we study a remarkably simple, low-dimensional, single-parameter family of quantum channels with exotic quantum information-theoretic features. As the simplest example from this family, we focus on a qutrit-to-qutrit channel that is intuitively obtained by hybridizing together a simple degradable channel and a completely useless qubit channel. Such hybridizing makes this channel’s capacities behave in a variety of interesting ways. For instance, the private and classical capacity of this channel coincide and can be explicitly calculated, even though the channel does not belong to any class for which the underlying information quantities are known to be additive. Moreover, the quantum capacity of the channel can be computed explicitly, given a clear and compelling conjecture is true. This “spin alignment conjecture,” which may be of independent interest, is proved in certain special cases and additional numerical evidence for its validity is provided. Finally, we generalize the qutrit channel in two ways, and the resulting channels and their capacities display similarly rich behavior. In a companion paper, we further show that the qutrit channel demonstrates superadditivity when transmitting quantum information jointly with a variety of assisting channels, in a manner unknown before.