Optimal verification of entangled states with local measurements

TL;DR

This paper identifies optimal local measurement strategies for verifying entangled two-qubit states, significantly reducing the number of measurements needed compared to traditional methods like tomography or Bell tests.

Contribution

It determines the optimal local verification strategy for two-qubit entangled states and shows it outperforms existing methods in measurement efficiency.

Findings

Quadratically fewer measurements needed for verification

Optimal strategies for stabilizer states provided

Local, non-adaptive measurements nearly as effective as unrestricted strategies

Abstract

Consider the task of verifying that a given quantum device, designed to produce a particular entangled state, does indeed produce that state. One natural approach would be to characterise the output state by quantum state tomography; or alternatively to perform some kind of Bell test, tailored to the state of interest. We show here that neither approach is optimal amongst local verification strategies for two qubit states. We find the optimal strategy in this case and show that quadratically fewer total measurements are needed to verify to within a given fidelity than in published results for quantum state tomography, Bell test, or fidelity estimation protocols. We also give efficient verification protocols for any stabilizer state. Additionally, we show that requiring that the strategy be constructed from local, non-adaptive and non-collective measurements only incurs a constant-factor penalty over a strategy without these restrictions.