Consider an open quantum system with (discrete-time) Markovian dynamics. Our task is to store information in the system in such a way that it can be retrieved perfectly, even after the system is left to evolve for an arbitrarily long time. We show that this is impossible for classical (resp. quantum) information precisely when the dynamics is mixing (resp. asymptotically entanglement breaking). Furthermore, we provide tight universal upper bounds on the minimum time after which any such dynamics `scrambles' the encoded information beyond the point of perfect retrieval. On the other hand, for dynamics that are not of this kind, we show that information must be encoded inside the peripheral space associated with the dynamics in order for it to be perfectly recoverable at any time in the future. This allows us to derive explicit formulas for the maximum amount of information that can be protected from noise in terms of the structure of the peripheral space of the dynamics.

翻译：考虑一个具有（离散时间）马尔可夫动力学的开放量子系统。我们的任务是以一种方式在系统中存储信息，使得即使系统经过任意长时间的演化，信息仍能被完美地检索。我们证明，当动力学是混合的（相应地，渐近纠缠破坏的）时，经典（相应地，量子）信息的完美存储与检索恰好是不可能的。此外，我们提供了紧致的普适上界，用于描述任何此类动力学在超过该时间后会将编码信息"扰乱"至无法完美检索的程度。另一方面，对于不属于此类的动力学，我们证明信息必须编码在与动力学相关的边缘空间内，才能在未来任意时刻被完美恢复。这使得我们能够根据动力学边缘空间的结构，推导出可被保护免受噪声影响的最大信息量的显式公式。