Verifying W states via 2-local symmetry tests with constant copy complexity

Quantum state verification is a statistically reliable way to test whether an experimental device prepares a desired quantum state, without reconstructing the full density matrix. We study nonadaptive, single-copy verification of the W state. Motivated by the recent Bell-matching verification for GHZ states, we introduce an analogous verifier based on disjoint two-qubit measurements. Increasing the allowed measurement locality by just one makes the spectral gap bounded away from zero. Consequently, the copy complexity becomes independent of the number of qubits. The same measurement also yields a fidelity estimation algorithm. By retaining an additional indicator from the outcome, we obtain an unbiased estimator of the W-state fidelity with copy complexity independent of the number of qubits.