Quantum metrology with N-qubit W superposition state under local and nonlocal operation

Abstract We study the performance of N-qubit W superposition state in quantum metrology. Taking advantage of the general Ising-type Hamiltonian (including local and nonlocal operation), we analytically present the Quantum Fisher information (QFI) of N-qubit W superposition state under different situations and then investigate its phase sensitivity. The results show that the phase sensitivity under local operation displays a crossover from W state to GHZ state, where it is same as W state in few-qubit case (N ≤ 6) but asymptotically equal to GHZ state for large qubit case (N >> 1). Interestingly, the 4-qubit W superposition state is found to have the same sensitivity with 4-qubit GHZ state, but be more robust than latter. Besides, the optimal theoretical proposals are provided for ideal metrology. Under the phase/amplitude damping channel, the phase sensitivity of W superposition state (except for N=3) is ultimately decreased to standard quantum limit, while it turns worse in depolarizing channel. Finally, the tunable phase sensitivity under nonlocal operation is studied and the general Heisenberg limit is surpassed with the increasing interaction strength γ . Meanwhile, a plateau of QFI and phase sensitivity is found for all large qubit W superposition state, which is similar to the study of GHZ state and again verifies the common feature of GHZ-type states in quantum metrology.