We investigate the entanglement robustness of an N-qubit W superposition state against particle loss with quantum Fisher information. In the noninteracting environment, the quantum Fisher information of reduced W superposition state is found same as it from W superposition state when the number of qubits is larger than 5, which shows very strong entanglement robustness compared to Twin-Fock state and Greenberger-Horne-Zeilinger state. Meanwhile, the re-particle-loss effect is also studied and it presents a rapid decay of quantum Fisher information with the increase of the number of losing qubits, indicating the weak entanglement robustness. In the Ising-type interacting environment, the results show that reduced W superposition state performs better than it in noninteracting environment. With the increasing qubits (N>5) the reduced W superposition state behaves much more robust than original W state. To simulate a real noisy environment, the effects of different decoherence channels are also considered.
Abstract We investigate the entanglement robustness of N-qubit W superposition state against particle loss with quantum Fisher information. In the noninteracting environment, the quantum Fisher information of reduced W superposition state is found same as the W superposition state when the number of qubits larger than 5, which shows very strong entanglement robustness compared to Twin-Fock state and Greenberger-Horne-Zeilinger state. Meanwhile, the effect of re-particle-loss is also studied and it presents a rapid decay of quantum Fisher information with the increase of losing qubits, indicating the weak entanglement robustness. In the interacting environment, the results show that the reduced W superposition state performs better than it in noninteracting environment. Alternatively, with the increase of qubits (N > 5) the reduced W superposition state behaves much more robust than original state. To vividly approach the real noisy environment, the effects of different decoherence channels are also considered.
In practice, the interaction between quantum system and environment will lead to the decoherence of entanglement. By quantifying the entanglement through the correlation tensor, we systematically investigate the entanglement robustness of two-qubit states under the four types of noisy channels and corresponding correlated channels. We use an analytical method to find all of the most robust and fragile states under the noisy channels. The puzzling phenomenon that the most robust and fragile states have the same entanglement under noisy channels has been investigated. Moreover, we compare the entanglement robustness of a three-qubit Greenberger-Horne-Zeilinger state with a
W state. Our method shows the behavior of entanglement under the noisy channels and characterizes the entanglement robustness of the multiqubit system analytically.
We study the performance of an
N-qubit
W superposition state composed of a
W state and its obverse in quantum metrology. Taking advantage of the general Ising-type Hamiltonian (including noninteracting and interacting operation), we analytically present the quantum Fisher information (QFI) of an
N-qubit
W superposition state under different situations and then investigate its phase sensitivity. The results show that the phase sensitivity under noninteracting operation displays a crossover from the
W state to Greenberger-Horne-Zeilinger (GHZ) state, where it is same as
W state in the few-qubit case $(N\ensuremath{\le}6)$ but asymptotically equal to the GHZ state for large-qubit cases $(N\ensuremath{\gg}1)$. Interestingly, the 4-qubit
W superposition state is found to have the same sensitivity as the 4-qubit GHZ state. And the optimal measurement protocols are provided for ideal metrology. Under the phase-amplitude damping channel, the phase sensitivity of the
W superposition state (except for
N=3) is ultimately decreased to the standard quantum limit, while it turns worse in a depolarizing channel. Finally, the tunable phase sensitivity under interacting operation is studied, and the general Heisenberg limit is surpassed with the increasing interaction strength $\ensuremath{\gamma}$. Meanwhile, a plateau of QFI and phase sensitivity is found for all large-qubit
W superposition states, which is similar to the study of the GHZ state and again verifies the common feature of GHZ-type states in quantum metrology.
Quantum fisher information of a parameter characterizing the sensitivity of a state with respect to parameter changes. In this paper, we study the quantum fisher information of the W state for four, five, six and seven particles in decoherence channels, such as amplitude damping, phase damping and depolarizing channel. Using Krauss operators for decoherence channels components, we investigate the quantum fisher information quite analytically. We observe that for the W state, the amount of the quantum fisher information and consequently, the amount of entanglement are reduced by applying the quantum noises, which affect each particle in the same way. In some cases, a relative increase appears in the quantum fisher information for certain values of the decay strength p. We also show that the phase damping channel vanishes the value of the quantum fisher information for the W state.
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.
Abstract Various quantum states have been suggested to realize high-precision measurement and quantum Fisher information (QFI) is one of the most important indicators to evaluate the performance. Here, we systematically investigate the QFI of an N-qubit maximal sliced (MS) state in different environments. In the ideal situation, we present the analytical QFI and it decays from N2 to (N − 1)2 as the parameter α changed from 0 to 1, which denotes the decreased metrological ability. In the amplitude damping channel, the variation trends of QFI with respect to p are similar and it decreases to the number of qubits N at p = 1, meaning the vanished entanglement superiority. However, it is different in the phase damping channel where with the increase of the number of qubits a turning point of QFI equal to N is found at p closing to 0.1. In the Ising-type interacting model, with the increasing interaction strength γ, the QFI with respect to α shows a crossover from decreasing to increasing. Particularly, at the critical point γ = 1, the QFI of an N-qubit MS state is found analytically equal to N2 and regardless of α. This indicates a great potential in achieving the Heisenberg-limited metrology and may shed some new light on quantum information science. PACS: 03.67.-a, 03.65.Ud