The efficient and reliable verification of quantum states plays a crucial role in various quantum information processing tasks. We consider the task of verifying entangled states using one-way and two-way classical communication and completely characterize the optimal strategies via convex optimization. We solve these optimization problems using both analytical and numerical methods, and the optimal strategies can be constructed for any bipartite pure state. Compared with the nonadaptive approach, our adaptive strategies significantly improve the efficiency of quantum state verification. Moreover, these strategies are experimentally feasible, as only few local projective measurements are required.

量子态的有效和可靠验证在各种量子信息处理任务中起着至关重要的作用。我们考虑了使用单向和双向经典通信验证纠缠态的任务，并通过凸优化完全表征了最优策略。我们使用解析和数值方法来解决这些优化问题，并且可以为任何二分纯态构造最优策略。与非自适应方法相比，我们的自适应策略显着提高了量子态验证的效率。而且，这些策略在实验上是可行的，因为仅需要很少的局部投影测量。