短时间下的序列传输
Sequential transmission at short times
AI总结：
该研究针对离散量子马尔可夫半群建模的n重复合量子信道，通过穿插量子纠错实现短时间信息传输与纠缠生成，推导了单次量子容量下界，明确传输速率与信道谱的关联，给出纯损耗信道等的误差界。
摘要：
我们证明，在建模为离散量子马尔可夫半群的n重复合量子信道$(Ξ^n)_{n \in \mathbb{N}}$上，能够在短时间尺度内传输并保存信息，且持续时间足以在某个有限n值下产生纠缠。这一结果通过在噪声作用过程中依次穿插量子纠错操作实现。我们通过推导序列场景下单次量子容量作为n的函数的非平凡下界来证明上述结论，旨在建模线性量子网络并评估其分发纠缠的能力。有趣的是，这类网络的传输速率被证明是序列组合信道的谱的固有属性，且传输的最大可能误差可仅由噪声模型的函数给出界。作为应用，我们推导了无限维纯损耗信道（pure-loss channel）的精确误差界，该信道被认为是阻碍纠缠分发的网络中噪声的主要来源。我们通过分析振幅阻尼信道（amplitude damping channel）及其玻色对应信道来例证我们的结果。
英文摘要：
We show that it is possible to transmit and preserve information at short time scales over an n-fold composition of quantum channels $(Ξ^n)_{n \in \mathbb{N}}$ modelled as a discrete quantum Markov semigroup, long enough to generate entanglement at some finite $n$. This is achieved by interspersing the action of noise with quantum error correction in succession. We show this by means of a non-trivial lower bound on the one-shot quantum capacity in the sequential setting as a function of $n$, in an attempt to model a linear quantum network and assess its capabilities to distribute entanglement. Intriguingly, the rate of transmission of such a network turns out to be a property of the spectrum of the channels composed in sequence, and the maximum possible error in transmission can be bounded as a function of the noise model only. As an application, we derive an exact error bound for the infinite dimensional pure-loss channel believed to be the dominant source of noise in networks precluding the distribution of entanglement. We exemplify our results by analysing the amplitude damping channel and its bosonic counterpart.
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