We establish a convex resource theory of non-Markovianity inducing information backflow under the constraint of small time intervals within the temporal evolution. We identify the free operations and a generalized bona-fide measure of non-Markovian information backflow. The framework satisfies the basic properties of a consistent resource theory. The proposed resource quantifier is lower bounded by the optimization free Rivas–Huelga–Plenio (RHP) measure of non-Markovianity. We next define the robustness of non-Markovianity and show that it can directly linked with the RHP measure of non-Markovianity through a lower bound. This enables a physical interpretation of the RHP measure. We further relate robustness of non-Markovianity with the quantum capacity of dephasing channels.

我们建立了一个非马尔可夫性的凸资源理论，它在时间演化的小时间间隔的约束下诱发信息回流。我们确定了自由操作和非马尔可夫信息回流的广义善意度量。该框架满足一致资源理论的基本属性。拟议的资源量词由非马尔可夫性的免费优化Rivas-Huelga-Plenio（RHP）度量来界定。接下来，我们定义非马尔可夫性的鲁棒性，并表明它可以通过下限与RHP度量非马尔可夫性直接相关。这使得能够对RHP度量进行物理解释。我们进一步将非马尔可夫性的鲁棒性与移相信道的量子容量联系起来。