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Potential Capacities of Quantum Channels

机译：量子通道的潜在容量

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We introduce potential capacities of quantum channels in an operational way and provide upper bounds for these quantities, which quantify the ultimate limit of usefulness of a channel for a given task in the best possible context. Unfortunately, except for a few isolated cases, potential capacities seem to be as hard to compute as their plain analogues. We thus study upper bounds on some potential capacities. For the classical capacity, we give an upper bound in terms of the entanglement of formation. To establish a bound for the quantum and private capacity, we first lift the channel to a Hadamard channel and then prove that the quantum and private capacity of a Hadamard channel is strongly additive, implying that for these channels, potential and plain capacity are equal. Employing these upper bounds, we show that if a channel is noisy, however close it is to the noiseless channel, then it cannot be activated into the noiseless channel by any other contextual channel; this conclusion holds for all the three capacities. We also discuss the so-called environment-assisted quantum capacity, because we are able to characterize its potential version.
机译：我们以一种可操作的方式介绍了量子通道的潜在容量，并提供了这些数量的上限，从而在最佳可能的情况下量化了通道对于给定任务有用性的最终极限。不幸的是，除了少数几个孤立的案例，潜在的能力似乎像普通的能力一样难以计算。因此，我们研究了一些潜在能力的上限。对于经典容量，我们在形成纠缠方面给出了上限。为了建立量子容量和私有容量的界限，我们首先将通道提升到Hadamard通道，然后证明Hadamard信道的量子容量和私有容量是可加性的，这意味着对于这些通道，潜在容量和普通容量是相等的。利用这些上限，我们表明，如果某个信道有噪声，但是无论它与无噪声信道有多近，那么它就不能被任何其他上下文信道激活到无噪声信道中。这个结论适用于所有三种能力。我们还讨论了所谓的环境辅助量子容量，因为我们能够表征其潜在版本。

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