We study the information transmission capacities of quantum Markov semigroups $(\Psi^t)_{t\in \mathbb{N}}$ acting on $d-$dimensional quantum systems. We show that, in the limit of $t\to \infty$, the capacities can be efficiently computed in terms of the structure of the peripheral space of $\Psi$, are strongly additive, and satisfy the strong converse property. We also establish convergence bounds to show that the infinite-time capacities are reached after time $t\gtrsim d^2\ln (d)$. From a data storage perspective, our analysis provides tight bounds on the number of bits or qubits that can be reliably stored for long times in a quantum memory device that is experiencing Markovian noise. From a practical standpoint, we show that typically, an $n-$qubit quantum memory, with Markovian noise acting independently and identically on all qubits and a fixed time-independent global error correction mechanism, becomes useless for storage after time $t\gtrsim n2^{2n}$. In contrast, if the error correction is local, we prove that the memory becomes useless much more quickly, i.e., after time $t\gtrsim \ln(n)$. In the setting of point-to-point communication between two spatially separated parties, our analysis provides efficiently computable bounds on the optimal rate at which bits or qubits can be reliably transmitted via long Markovian communication channels $(\Psi^l)_{l\in \mathbb{N}}$ of length $l\gtrsim d^2 \ln(d)$, both in the finite block-length and asymptotic regimes.

翻译：我们研究了作用于$d$维量子系统的量子马尔可夫半群$(\Psi^t)_{t\in \mathbb{N}}$的信息传输容量。我们证明，在$t\to \infty$的极限下，容量可以根据$\Psi$的周边空间结构进行高效计算，具有强可加性，并满足强逆性质。我们还建立了收敛界，表明无限时间容量在$t\gtrsim d^2\ln (d)$后达到。从数据存储的角度看，我们的分析为在经历马尔可夫噪声的量子存储设备中长期可靠存储的比特或量子比特数量提供了紧致界。从实际角度出发，我们证明：对于具有马尔可夫噪声（独立同等地作用于所有量子比特）和固定时间无关全局纠错机制的$n$量子比特量子存储器，通常在$t\gtrsim n2^{2n}$时间后即丧失存储功能。相反，若纠错机制是局部的，我们证明存储器失效速度显著加快，即在$t\gtrsim \ln(n)$时间后失效。在两个空间分离方之间的点对点通信场景中，我们的分析为通过长度$l\gtrsim d^2 \ln(d)$的长马尔可夫通信信道$(\Psi^l)_{l\in \mathbb{N}}$可靠传输比特或量子比特的最优速率提供了高效可计算的界，该结果同时适用于有限块长度与渐近区域。