Entanglement is a quantum resource, in some ways analogous to randomness in classical computation. Inspired by recent work of Gheorghiu and Hoban, we define the notion of "pseudoentanglement'', a property exhibited by ensembles of efficiently constructible quantum states which are indistinguishable from quantum states with maximal entanglement. Our construction relies on the notion of quantum pseudorandom states -- first defined by Ji, Liu and Song -- which are efficiently constructible states indistinguishable from (maximally entangled) Haar-random states. Specifically, we give a construction of pseudoentangled states with entanglement entropy arbitrarily close to $\log n$ across every cut, a tight bound providing an exponential separation between computational vs information theoretic quantum pseudorandomness. We discuss applications of this result to Matrix Product State testing, entanglement distillation, and the complexity of the AdS/CFT correspondence. As compared with a previous version of this manuscript (arXiv:2211.00747v1) this version introduces a new pseudorandom state construction, has a simpler proof of correctness, and achieves a technically stronger result of low entanglement across all cuts simultaneously.

翻译：纠缠是一种量子资源，在某种程度上类似于经典计算中的随机性。受Gheorghiu和Hoban近期工作的启发，我们定义了“伪纠缠”的概念——这一性质由可高效构造的量子态系综展现，且此类态与具有最大纠缠的量子态不可区分。我们的构造依赖于量子伪随机态（最早由Ji、Liu和Song定义）的概念，即与（最大纠缠的）Haar随机态不可区分的可高效构造量子态。具体而言，我们给出了一个伪纠缠态的构造，其纠缠熵在每个截面处均任意接近$\log n$，这一紧界为计算与信息论量子伪随机性之间提供了指数级分离。我们讨论了该结果在矩阵乘积态测试、纠缠蒸馏以及AdS/CFT对应复杂性中的应用。与本文先前版本（arXiv:2211.00747v1）相比，本版本引入了新的伪随机态构造，具有更简洁的正确性证明，并在所有截面上同时实现了技术上更强的低纠缠结果。