Efficient verification of arbitrary entangled states with homogeneous local measurements

TL;DR

This paper introduces a systematic method for verifying any entangled quantum state using homogeneous local measurements, improving efficiency and extending to other quantum information tasks.

Contribution

It presents a new strategy for designing verification protocols for arbitrary entangled states based on homogeneous local measurements, which was previously an open problem.

Findings

Protocol design using standard Pauli projections demonstrated for typical states

Method achieves better quantum state verification strategies

Framework extends to entanglement witness construction and parameter estimation

Abstract

Quantum state verification (QSV) is the task of relying on local measurements only to verify that a given quantum device does produce the desired target state. Up to now, certain types of entangled states can be verified efficiently or even optimally by QSV. However, given an arbitrary entangled state, how to design its verification protocol remains an open problem. In this work, we present a systematic strategy to tackle this problem by considering the locality of what we initiate as the choice-independent measurement protocols, whose operators can be directly achieved when they are homogeneous. Taking several typical entangled states as examples, we show the explicit procedures of the protocol design using standard Pauli projections, demonstrating the superiority of our method for attaining better QSV strategies. Moreover, our framework can be naturally extended to other tasks such as the construction of entanglement witness, and even parameter estimation.