Quantum systems may contain underlying correlations which are inaccessible to computationally bounded observers. We capture this distinction through a framework that analyses bipartite states only using efficiently implementable quantum channels. This leads to a complexity-constrained max-divergence and a corresponding computational min-entropy. The latter quantity recovers the standard operational meaning of the conditional min-entropy: in the fully quantum case, it quantifies the largest overlap with a maximally entangled state attainable via efficient operations on the conditional subsystem. For classical-quantum states, it further reduces to the optimal guessing probability of a computationally bounded observer with access to side information. Lastly, in the absence of side information, the computational min-entropy simplifies to a computational notion of the operator norm. We then establish strong separations between the information-theoretic and complexity-constrained notions of min-entropy. For pure states, there exist highly entangled families of states with extremal min-entropy whose efficiently accessible entanglement in terms of computational min-entropy is exponentially suppressed. For mixed states, the separation is even sharper: the information-theoretic conditional min-entropy can be highly negative while the complexity-constrained quantity remains nearly maximal. Overall, our results demonstrate that computational constraints can fundamentally limit the quantum correlations that are observable in practice.

翻译：量子系统中可能存在着计算能力有限的观察者无法访问的潜在关联。我们通过一个框架来捕捉这种区别，该框架仅使用可高效实现的量子通道来分析双粒子态。这引出了复杂度约束的最大散度以及相应的计算最小熵。后者恢复了条件最小熵的标准操作意义：在全量子情形下，它量化了通过对条件子系统进行高效操作所能达到的最大纠缠态重叠量。对于经典-量子态，它进一步简化为具有侧信息的计算能力有限观察者的最优猜测概率。最后，在没有侧信息的情况下，计算最小熵简化为算子范数的计算概念。然后，我们建立了信息论与复杂度约束下最小熵概念之间的强分离性。对于纯态，存在具有极端最小熵的高度纠缠态族，其基于计算最小熵的高效可访问纠缠性呈指数级抑制。对于混合态，这种分离更为显著：信息论条件最小熵可能高度负值，而复杂度约束量仍保持近似最大值。总的来说，我们的结果表明计算约束本质上限制了实践中可观测的量子关联。