Efficient verification of arbitrary entangled states with homogeneous local measurements

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.