# Experimental Optimal Verification of Entangled States using Local Measurements

## TL;DR

This paper experimentally demonstrates an optimal, robust method for verifying entangled quantum states using only local measurements, achieving high efficiency with minimal measurement resources.

## Contribution

The authors implement a locally measured, optimal quantum state verification method that is robust, efficient, and nearly as effective as nonlocal strategies, reducing resource requirements.

## Key findings

- Infidelity inversely proportional to the number of measurements
- Method tolerant to state impurity
- Local measurements incur less than 2.5 times the resource cost of global strategies

## Abstract

The initialization of a quantum system into a certain state is a crucial aspect of quantum information science. While a variety of measurement strategies have been developed to characterize how well the system is initialized, for a given one, there is in general a trade-off between its efficiency and the accessible information of the quantum state. Conventional quantum state tomography can characterize unknown states by reconstructing the density matrix; however, its exponentially expensive postprocessing is likely to produce a deviate result. Alternatively, quantum state verification provides a technique to quantify the prepared state with significantly fewer measurements, especially for quantum entangled states. Here, we experimentally implement an optimal verification of entangled states with local measurements, where the estimated infidelity is inversely proportional to the number of measurements. The utilized strategy is tolerant of the impurity of realistic states, hence being highly robust in a practical sense. Even more valuable, our method only requires local measurements, which incurs only a small constant-factor (<2.5) penalty compared to the globally optimal strategy requiring nonlocal measurements.