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arXiv:1808.04632 · Physical Review A

Multiqubit matter-wave interferometry under decoherence and the Heisenberg scaling recovery

Yanming Che, Jing Liu, Xiao-Ming Lu, Xiaoguang Wang

Published Mar 4, 2019• 13 citations
arXivHTMLPDF

Abstract

Most matter-wave interferometry (MWI) schemes for quantum sensing have so far been evaluated in ideal situations without noise. In this work, we provide assessments of generic multiqubit MWI schemes under Markovian dephasing noise. We find that, for certain classes of the MWI schemes with scale factors that are nonlinearly dependent on the interrogation time, the optimal precision of maximally entangled probes decreases with increasing particle number $N$, for both independent and collective dephasing situations. This result challenges the conventional wisdom found in dephasing Ramsey-type interferometers. We initiate the analyses by investigating the optimal precision of multiqubit Sagnac atom interferometry for rotation sensing. And we show that, due to the competition between the unconventional interrogation-time quadratic phase accumulation and the exponential dephasing processes, the Greenberger--Horne--Zeilinger (GHZ) state, which is the optimal input state in noiseless scenarios, leads to vanishing quantum Fisher information in the large-$N$ regime. Then our assessments are further extended to generic MWI schemes for quantum sensing with entangled states and under decoherence. Finally, a quantum error-correction logical GHZ state is tentatively analyzed, which could have the potential to recover the Heisenberg scaling and improve the sensitivity.

DOI
10.1103/physreva.99.033807

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Most matter-wave interferometry (MWI) schemes for quantum sensing have so far been evaluated in ideal situations without noise. In this work, we provide assessments of generic multiqubit MWI schemes under Markovian dephasing noise. We find that, for certain classes of the MWI schemes with scale factors that are nonlinearly dependent on the interrogation time, the optimal precision of maximally entangled probes decreases with increasing particle number NNN, for both independent and collective dephasing situations. This result challenges the conventional wisdom found in dephasing Ramsey-type interferometers. We initiate the analyses by investigating the optimal precision of multiqubit Sagnac atom interferometry for rotation sensing. And we show that, due to the competition between the unconventional interrogation-time quadratic phase accumulation and the exponential dephasing processes, the Greenberger--Horne--Zeilinger (GHZ) state, which is the optimal input state in noiseless scenarios, leads to vanishing quantum Fisher information in the large-NNN regime. Then our assessments are further extended to generic MWI schemes for quantum sensing with entangled states and under decoherence. Finally, a quantum error-correction logical GHZ state is tentatively analyzed, which could have the potential to recover the Heisenberg scaling and improve the sensitivity.
Interactions among sensors can provide, in addition to entanglement, an important resource for boosting the precision in quantum estimation protocols. Dephasing noise, however, remains a leading source of decoherence in state-of-the-art quantum sensing platforms. We analyze the impact of classical collective dephasing with arbitrary temporal correlations on the performance of generalized Ramsey interferometry protocols with quadratic encoding of a target frequency parameter. The optimal asymptotic precision bounds are derived for both product coherent spin states and a class of experimentally relevant entangled spin-squeezed states of N qubit sensors. While, as in linear metrology, entanglement offers no advantage if the noise is Markovian, a precision scaling of N−1 is reachable with classical input states in the quadratic setting, which is improved to N−5/4 when temporal correlations are present and the Zeno regime is accessible. The use of nonclassical spin-squeezed states and a nonlinear readout further allows for an N−3/2 precision scaling, which we prove is asymptotically optimal. We also show how to counter noise-induced bias by introducing a simple ratio estimator, which relies on detecting two suitable system observables, and we show that it remains asymptotically unbiased in the presence of dephasing, without detriment to the achievable precision.
Dephasing noise is a ubiquitous source of decoherence in current atomic sensors. We address the problem of entanglement-assisted frequency estimation subject to classical dephasing noise with full spatial correlations (collective) and arbitrary temporal correlations. Our contributions are threefold. (i) We derive rigorous, state-independent bounds on the achievable estimation precision, showing how they are entirely determined by the short-time behavior of the decoherence function. For temporally uncorrelated (Markovian) dephasing, precision is limited by a probe-independent constant. For temporally correlated stationary noise, the bound approaches the noiseless limit for classical states, precluding any asymptotic quantum advantage. (ii) We show that these scaling bounds are tight, by constructing generalized Ramsey protocols that saturate them. These optimal protocols use squeezing at the input and before readout, both of which are available in state-of-the-art atomic interferometers. Implementing a perfect-echo protocol, which reaches Heisenberg scaling in the absence of noise, remains optimal in this noisy setting, irrespective of the noise temporal correlations. (iii) We prove that arbitrary collective open-loop control cannot lift the no-go for super-classical precision scaling under either Markovian or colored stationary noise, highlighting the detrimental nature of full spatial correlations. In the latter case, temporal correlations may nonetheless enable constant-factor improvements over the standard quantum limit, which may still be important in practical metrological scenarios.
Phase sensing with entangled multi-qubit states in the presence of noise is a central theme of modern quantum metrology. The present work investigates Dicke state superposition probes for quantum phase sensing under parameter encoding generated by one- and two-body interaction Hamiltonians. Under linear collective-spin encoding, near-optimal Dicke superposition states are shown to exhibit significantly enhanced robustness against phase damping noise compared with Greenberger--Horne--Zeilinger (GHZ), W-superposition, and balanced Dicke states, while maintaining favorable metrological performance under realistic decoherence channels. For two-body interactions, optimal probe states maximizing the quantum Fisher information are identified. Their noise resilience and metrological scaling behaviour under phase damping, amplitude damping, and global depolarizing channels are analyzed. The associated near-optimal Dicke superposition states are found to exhibit improved resilience to phase damping, for the system sizes considered. These results establish tailored near-optimal Dicke state superposition probes as versatile and noise-resilient resources for Heisenberg and super-Heisenberg quantum phase sensing governed by one- and two-body interactions.
Recently, a DC magnetometry protocol utilizing NNN-spin-ensemble superradiance was proposed. This method physically amplifies the acquired signal, suppressing estimation errors from measurement noise and achieving O(1/N)\mathcal{O}(1/N)O(1/N) precision scaling when measurement noise dominates quantum fluctuations. However, quantum metrology is generally vulnerable to independent Markovian pure dephasing. For instance, the scaling of Greenberger-Horne-Zeilinger (GHZ) state-based magnetometry deteriorates from O(1/N)\mathcal{O}(1/N)O(1/N) to O(1/N)\mathcal{O}(1/\sqrt{N})O(1/N​). Although pure dephasing likely degrades superradiant sensing, its quantitative impact remains unclear. Here, we investigate the effect of independent Markovian pure dephasing on this protocol using numerical simulations and mean-field analysis. We demonstrate that, in the large-NNN limit, the estimation error increase is limited to a constant factor. This sharply contrasts with GHZ-state-based sensing, where the error increases by a factor of N\sqrt{N}N​. Our analytical solutions elucidate the physical origin of this robustness qualitatively. These findings establish the high robustness of superradiance-based DC magnetometry against independent Markovian pure dephasing.
Quantum sensors have been shown to enable more precise measurements than classical sensors. By using entanglement and coherent evolution, the estimation error can be made to scale better in interrogation time, photon count, and other resources, achieving Heisenberg-limited scaling. However, environmental noise and hardware errors typically destroy the coherence of the sensitive quantum states. This motivates the use of fault-tolerant techniques to create more robust quantum sensing protocols. Such fault-tolerant quantum sensing approaches have been shown to enhance sensitivity for qubit systems, but many practical sensors require bosonic probes. In this paper, we propose a fault-tolerant protocol using bosons to estimate displacements in the presence of dephasing noise. We construct an optimal error-correcting code under a mean photon-number constraint. Controlled displacements couple the probe to a repetition-encoded qubit register, while repeated boson-parity measurements and resets remove probe noise without erasing the stored logical phase. Under circuit-level bit-flip noise, a distance-ddd code suppresses logical failures to order p(d+1)/2p^{(d+1)/2}p(d+1)/2. We show that, for a decay rate γAγ_AγA​, a total sensing time TTT and a mean photon number budget NNN, and for sufficiently small residual signals, the Fisher information scales as NT2NT^2NT2 over interrogation times of order γA−(d+1)/2γ_A^{-(d+1)/2}γA−(d+1)/2​. This is a significant improvement over the non-fault-tolerant approach that achieves Heisenberg scaling only for a total time O(γA−1)\mathcal O(γ_A^{-1})O(γA−1​).
Abstract Exploring the quantum advantages of various non-classical quantum states in noisy environments is a central subject in quantum sensing. Here we provide a complete picture for the frequency estimation precision of three important states (the Greenberger–Horne–Zeilinger (GHZ) state, the maximal spin squeezed state, and the spin coherent state) of a spin-S under both individual dephasing and collective dephasing by general Gaussian noise, ranging from the Markovian limit to the extreme non-Markovian limit. Whether or not the noise is Markovian, the spin coherent state is always worse than the classical scheme under collective dephasing although it is equivalent to the classical scheme under individual dephasing. Moreover, the maximal spin squeezed state always give the best sensing precision (and outperforms the widely studied GHZ state) in all cases. This establishes the general advantage of the spin squeezed state for noisy frequency estimation in many quantum sensing platforms.