Improving quantum communication rates with permutation-invariant codes
中文速览 本文提出了一种新方法，利用一类具有排列对称性的量子编码来提升各种有噪量子信道的通信速率。核心思想是，独立同分布（i.i.d.）的量子信道会保持输入态的排列不变性。作者利用对称群与一般线性群的表示论（特别是舒尔-外尔对偶性），将计算相干信息这一复杂问题转化为一个在多项式时间内可解的表示论问题。这种方法使得对大量信道副本（例如，对于量子比特信道可达100个副本）进行优化成为可能。通过将此方法应用于多种重要的信道模型（如泡利信道、去相位擦除信道和广义幅度阻尼信道），作者显著提高了已知的量子容量下界和阈值。一个关键发现是，使用非正交的基态构成的“重复码”在某些信道（如2-泡利信道和BB84信道）上，其性能优于传统的正交重复码。 English Research Briefing Research Briefing: Improving quantum communication rates with permutation-invariant codes 1. The Core Contribution This paper introduces a powerful computational framework for finding high-performing quantum codes that improve communication rates through noisy channels. The central thesis is that by restricting the search to permutation-invariant codes, specifically convex mixtures of independent and identically distributed (i.i.d.) states, one can leverage the tools of representation theory to efficiently calculate the channel’s coherent information for a large number of channel uses. The primary conclusion is that this method yields significantly improved lower bounds on the quantum capacity and, more importantly, the quantum capacity thresholds for several physically relevant channels known to exhibit superadditivity. A key and non-intuitive finding is the discovery that non-orthogonal repetition codes (codes built from non-orthogonal basis states) can substantially outperform standard orthogonal repetition codes, establishing a new and simple design principle for enhancing quantum communication. ...