Abstract From the perspective of nonlocal operation, we investigate the Quantum Fisher information of N-qubit W and GHZ superposition state. Taking advantage of the general Ising model and Lipkin-Meshkov-Glick model, we analytically present the QFI of N-qubit superposition state. Evidently the traditional fixed QFI is changed and largely increased. As an paradigm, we numerically study the QFI of 3-qubit superposition state with respect to ratio α and interaction strength ε, and find the trends of QFI in both models are similar. There always exists a turning point for QFI and the α is around 0.7. Interestingly, for the interaction strength ε = 1 in Ising model, the well-known Heisenberg limit is almost achieved for all α. Moreover, under the same interaction strength, we compare the QFI of N-qubit superposition state in both models. With the increasing qubits involved, the α for maximal QFI in Ising model is changed from close to 1 to the middle region, while it is different in Lipkin-Meshkov-Glick model and the α is close to 1.
Abstract From the perspective of nonlocal operation, we investigate the Quantum Fisher information of N-qubit W and GHZ superposition state. Taking advantage of the general Ising model and Lipkin-Meshkov-Glick model, we analytically present the QFI of N-qubit superposition state. Evidently the traditional fixed QFI is changed and largely increased. As an paradigm, we numerically study the QFI of 3-qubit superposition state with respect to ratio α and interaction strength ε, and find the trends of QFI in both models are similar. There always exists a turning point for QFI and the α is around 0.7. Interestingly, for the interaction strength ε = 1 in Ising model, the well-known Heisenberg limit is almost achieved for all α. Moreover, under the same interaction strength, we compare the QFI of N-qubit superposition state in both models. With the increasing qubits involved, the α for maximal QFI in Ising model is changed from close to 1 to the middle region, while it is different in Lipkin-Meshkov-Glick model and the α is close to 1.
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
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.
Abstract We study the metrological performance of the superposition of Greenberger-Horne-Zeilinger state and Twin Fock state (SGT) in quantum phase estimation. The analytical quantum Fisher information (QFI) of an Nqubit SGT state in noninteracting environment has been derived and with the increasing ratio β in SGT state it emerges a turning point at βt = q 1 − 1 N · q2 3 , where the smallest QFI FQ = (N 2 + 2N)/3 is achieved. Interestingly, we find the 4-qubit SGT state performs better than TF state in all ratio region and further achieves the Heisenberg limit at β = √ 3/2. Working in the Mach-Zehnder interferometry, we have provided the optimal metrology schemes saturated by quantum CRLB for all kinds of SGT states and found the same βt also existed in the selection of phase generator and measured parity operator. Moreover, we have considered the decoherence effects and with the increasing decay the QFI in amplitude damping and phase damping channel decreases to the number of qubits involved, while it decreases to zero in depolarizing channel. Specially, the 4-qubit SGT state of β = √ 3/2 is found to perform better than GHZ state in phase damping channel. Our work enriches the metrological useful quantum resources.
We examine the metrological performance of WW¯-like state (αWN+βW¯N) in quantum phase estimation. Based on the framework of quantum interferometry, we analytically derive the quantum Fisher information (QFI) and analyze the precision limits. In the noninteracting environment, the metrological power of WW¯-like state is same as that of the W state in few-qubit case but symmetrically enhanced (with respect to β2) in large-qubit case. In the Ising model, with increasing interaction strength, the QFI of N≤6 qubit WW¯-like state is universally enhanced and displays different and exotic trends (with respect to β2), particularly for 4- and 6-qubit cases where it respectively shows a reversible phenomenon and a reversal scenario. Regarding others (N>6), it exhibits a similar trend that the precision limit is always better than that of WW¯ state in strong interaction.
Abstract We comprehensively study the metrological performance of perfect W (PW) state in quantum phase measurement, including local operation and two-body interacting operation as the phase generator. The analytical precision limits are obtained in both cases and the decoherence effects are also investigated. The results show that under local operation the precision limit is slightly lower than it from W state, indicating the weaker sensitivity. Specially, with increasing m the precision limit from the general 3-qubit PW state approaches 1/Sqrt{5}. In the amplitude damping channel, the precision limit decreases first and then increases to the shot noise limit, whereas it is always decreased in phase damping channel. Alternatively, we have also provided the optimal strategies for quantum phase estimation. In the two-body interacting operations, Ising model and Lipkin-Meshkov-Glick (LMG) model are employed to explore the precision limit with respect to interacting strength. It behaves similar in both cases that with increasing the precision limit surpasses the general Heisenberg limit and gradually converges with W state. However, the difference is also evident that the more qubits involved for achieving Heisenberg limit, the larger the needed \gamma in Ising model but smaller in LMG model. Interestingly, in amplitude damping channel, with increasing an expanding platform area of precision limit emerges in the few-qubit PW state (N < 6), while it gradually disappears in the large qubit case. This will be beneficial to the stable and tunable high-precision measurement, especially under the noisy circumstances.