# Optimal Verification of Two-Qubit Pure States

## TL;DR

This paper determines the optimal measurement strategies for verifying two-qubit pure states across various classes of LOCC and separable measurements, revealing two-way LOCC's equivalence to separable measurements in effectiveness.

## Contribution

It provides the first complete characterization of optimal verification strategies for two-qubit pure states among LOCC and separable measurement classes.

## Key findings

- Two-way LOCC matches separable measurements in verification efficiency.
- Two-way LOCC outperforms one-way LOCC in state verification.
- Optimal strategies depend on measurement class constraints.

## Abstract

In a recent work [Phys. Rev. Lett. 120, 170502 (2018)], Pallister et al. proposed an optimal strategy to verify non-maximally entangled two-qubit pure states under the constraint that the accessible measurements being locally projective and non-adaptive. Their nice result leads naturally to the question: What is the optimal strategy among general LOCC measurements? In this Letter, we answer this problem completely for two-qubit pure states. To be specific, we give the optimal strategy for each of the following available classes of measurements: (i) local operations and one-way classical communication (one-way LOCC) measurements; (ii) local operations and two-way classical communication (two-way LOCC) measurements; and (iii) separable measurements. Surprisingly, our results reveal that for the two-qubit pure state verification problem, two-way LOCC measurements remarkably outperforms one-way LOCC measurements and has the same power as the separable measurements.