Generic non-Markovian quantum processes have infinitely long memory, implying an exact description that grows exponentially in complexity with observation time. Here, we present a finite memory ansatz that approximates (or recovers) the true process with errors bounded by the strength of the non-Markovian memory. The introduced memory strength is an operational quantity and depends on the way the process is probed. Remarkably, the recovery error is bounded by the smallest memory strength over all possible probing methods. This allows for an unambiguous and efficient description of non-Markovian phenomena, enabling compression and recovery techniques pivotal to near-term technologies. We highlight the implications of our results by analyzing an exactly solvable model to show that memory truncation is possible even in a highly non-Markovian regime.

通用非马尔可夫量子过程具有无限长的记忆，这意味着精确描述的复杂性随着观察时间呈指数增长。在这里，我们提出了一个有限的记忆 ansatz，它近似（或恢复）真实过程，其误差受非马尔可夫记忆强度的限制。引入的内存强度是一个操作量，取决于探测过程的方式。值得注意的是，在所有可能的探测方法中，恢复误差受最小记忆强度的限制。这允许对非马尔可夫现象进行明确而有效的描述，从而实现对近期技术至关重要的压缩和恢复技术。我们通过分析一个完全可解的模型来强调我们的结果的含义，以表明即使在高度非马尔可夫制度中也可能发生内存截断。