Quantum Verification for a Class of n $n$ -Qubit Quantum Entangled States

The quantum verification is to determine whether a quantum device is intentionally deceptive by assessing the proximity between the actual output state and the expected state. As a crucial step toward the advancement of quantum technology, numerous quantum state verification methods have been proposed. However, there remains a scarcity of methods for verifying states with an arbitrary number of qubits. A verification strategy for the entangled states $|\psi ⟩=\sin \theta {|0⟩}^{\otimes n}+\cos \theta {|1⟩}^{\otimes n}$ with $\theta \in (0,\pi /2)$ is proposed. Specifically, an average map is introduced and demonstrated that it simplifies the matrix form of the verification strategy while maintaining the verification efficiency. By optimizing the verification strategies, the strategy with local projective measurements is obtained.