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.