[论文解读] Optimizing the fundamental limits for quantum and private communication

Xin Wang|arXiv (Cornell University)|Dec 2, 2019

Quantum Computing Algorithms and Architecture被引用 7

一句话总结

本文通过在具有特定结构的扩展通道（如标志结构）上进行优化，推导出量子通道的量子容量和隐私容量的新单字母上界。该方法所得上界比以往结果更紧，尤其在诸如去极化通道和广义衰减幅度通道等关键通道上表现更优。

ABSTRACT

The quantum capacity of a noisy quantum channel determines the maximal rate at which we can code reliably over asymptotically many uses of the channel, and it characterizes the channel's ultimate ability to transmit quantum information coherently. In this paper, we derive single-letter upper bounds on the quantum and private capacities of quantum channels. The quantum capacity of a quantum channel is always no larger than the quantum capacity of its extended channels since the extensions of the channel can be considered as assistance from the environment. By optimizing the parametrized extended channels with specific structures such as the flag structure, we obtain new upper bounds on the quantum capacity of the original quantum channel. Furthermore, we extend our approach to estimating the fundamental limits of private communication and one-way entanglement distillation. As notable applications, we establish improved upper bounds to the quantum and private capacities for fundamental quantum channels of great interest in quantum information, some of which are also the sources of noise in superconducting quantum computing. In particular, our upper bounds on the quantum capacities of the depolarizing channel and the generalized amplitude damping channel are strictly better than previously best-known bounds.

研究动机与目标

• 建立噪声量子通道上量子与隐私通信速率的更紧根本极限。
• 解决在噪声存在下量化量子通信性能极限的挑战。
• 通过利用原始通道的结构化扩展，改进现有量子容量上界。
• 将该框架扩展至隐私通信与单向纠缠纯化容量。

提出的方法

• 通过原始量子通道的扩展版本推导量子与隐私容量的单字母上界。
• 对具有特定结构（如标志结构）的参数化扩展通道进行优化，以收紧上界。
• 利用扩展通道的量子容量为原始通道容量提供上界的事实。
• 将该方法应用于超导量子计算中相关的基础量子通道，包括去极化通道与广义衰减幅度通道。
• 利用量子容量与隐私容量之间的对偶性，将结果扩展至隐私通信与纠缠纯化。

实验结果

研究问题

• RQ1 对于一般噪声量子通道，其量子容量的最紧可能单字母上界是什么？
• RQ2 如何利用量子通道的结构化扩展来推导其量子容量的改进上界？
• RQ3 通过该方法，对隐私通信与单向纠缠纯化容量的上界最多能收紧到何种程度？
• RQ4 与以往已知的上界相比，新上界在去极化通道与广义衰减幅度通道等基础通道上表现如何？

主要发现

• 所提方法得出的量子容量新单字母上界，对去极化通道而言严格优于以往最佳已知上界。
• 对于广义衰减幅度通道，新上界也严格优于早期结果。
• 该框架成功扩展至隐私通信，提供了隐私容量的改进上界。
• 该方法表明，结构化扩展（尤其是具有标志结构的扩展）可显著提升容量上界的紧致性。