# Optimal verification of general bipartite pure states

## TL;DR

This paper develops optimal strategies for verifying bipartite pure quantum states using classical communication, improving efficiency over nonadaptive methods and ensuring experimental feasibility through local measurements.

## Contribution

It provides a complete characterization and construction of optimal adaptive verification strategies for any bipartite pure state via convex optimization.

## Key findings

- Adaptive strategies outperform nonadaptive ones in efficiency.
- Optimal strategies are feasible with minimal local measurements.
- Both analytical and numerical solutions are provided.

## Abstract

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.