Dicke Superposition Probes Reveal N-Qubit Scaling for Resilient Heisenberg Metrology

Researchers are continually seeking methods to enhance the precision of measurements, and a new study details a promising approach using entangled quantum states. Sudha, B. N. Karthik, and K. S. Akhilesh, from Kuvempu University, alongside A. R. Usha Devi of Bangalore University, demonstrate the potential of Dicke superposition probes for highly accurate phase estimation, even when subjected to significant noise. Their work identifies specific Dicke states which not only approach the ultimate Heisenberg limit of precision but also exhibit greater robustness against dephasing and other common quantum errors than previously explored states. This finding is significant because it paves the way for more reliable and sensitive quantum sensors, potentially revolutionising fields reliant on precise measurements, such as medical imaging and materials science.

Dicke states enhance quantum sensing sensitivity and noise resilience by leveraging collective interactions

Scientists have demonstrated tailored near-optimal Dicke-state superposition probes as versatile and noise-resilient resources for Heisenberg and super-Heisenberg quantum phase sensing. The research investigates these probes for quantum phase sensing under parameter encoding generated by both one- and two-body interaction Hamiltonians, focusing on scaling of the quantum Fisher information and robustness against various noise types.
A class of N-qubit Dicke superposition states exhibiting near-Heisenberg scaling, with a quantum Fisher information of approximately N2, has been identified, while simultaneously maintaining enhanced robustness to dephasing noise when compared to Greenberger, Horne, Zeilinger, W-superposition, and balanced Dicke states. This achievement relies on unitary encodings generated by one-body interaction Hamiltonians, offering a significant improvement in sensitivity and stability.

The study establishes a framework for parameter estimation in quantum metrology, building upon the classical Cramér-Rao bound and extending it to the quantum realm with the quantum Fisher information. Researchers determined that the quantum Cramér-Rao bound sets a fundamental lower limit on the variance of any unbiased estimator of a parameter, and the quantum Fisher information quantifies the ultimate sensitivity of a probe state to parameter changes.

Experiments show that for N-qubit Dicke superposition states, the quantum Fisher information scales near-Heisenberg, approximately N2, indicating a substantial enhancement in precision compared to the standard quantum limit. This scaling is particularly notable under unitary encodings generated by one-body interaction Hamiltonians, where the probes exhibit improved resilience against dephasing noise.

For two-body interactions, the team identified Dicke superposition probes that optimize the quantum Fisher information, subsequently exploring their performance under phase-damping, amplitude-damping, and global depolarizing noise. Within this family of probes, certain Dicke superpositions combine super-Heisenberg scaling with improved resilience to phase damping relative to Fisher-information, optimal probes, representing a significant advancement in noise mitigation.

The work opens avenues for designing tailored quantum states that not only maximize sensitivity but also maintain performance in realistic noisy environments, crucial for practical applications of quantum metrology. These results establish that tailored near-optimal Dicke-state superposition probes are versatile resources for Heisenberg and super-Heisenberg quantum phase sensing governed by both one- and two-body interactions.

The research systematically investigates the metrological role of these tailored states in noisy settings, providing a comprehensive analysis of their scaling properties and noise robustness. By comparing the performance of Dicke superpositions with standard probes like GHZ and W states, the study highlights the advantages of engineered superpositions in achieving enhanced precision and resilience in quantum sensing applications.

Quantifying precision limits using Fisher information and the Cramer-Rao bound provides a fundamental approach to estimation theory

Scientists investigated Dicke state superposition probes for enhanced phase sensing, focusing on parameter encoding via one- and two-body interaction Hamiltonians. The study identified N-qubit Dicke superposition states exhibiting near-Heisenberg scaling of the Fisher information, alongside significantly improved robustness against dephasing noise when compared to GHZ, W-superposition, and balanced Dicke states under unitary encodings.

Researchers determined that these states offer a versatile resource for Heisenberg and super-Heisenberg phase estimation governed by both one- and two-body interactions. The work employed the quantum Cram er-Rao bound to define ultimate precision limits, beginning with preparation of input probe states and parameter encoding.

Experiments utilized the Fisher information, calculated as the classical Fisher information using probability distributions p(x|θ) and its derivative with respect to the parameter θ, to quantify estimation precision. Scientists then maximized this classical Fisher information over all possible positive-operator-valued measures to obtain the quantum Fisher information, establishing a fundamental lower bound on the variance of any unbiased estimator.

To characterize probe performance, the team calculated the QFI for both pure and mixed states, leveraging the variance of the Hamiltonian, ∆²H, and its eigenvalues, λmax and λmin. For pure states, the QFI was determined using the equation FQ(|ψ⟩, H) = 4 ∆²H, while for mixed states, the formula FQ(ρ, H) = 2Σ(λi −λj)² / (λi + λj) ⟨ψi| H|ψj⟩² was applied.

The optimal probe state, |ψ⟩opt = (|φmax⟩ + |φmin⟩) / √2, was identified as achieving maximal QFI, where |φmax⟩ and |φmin⟩ represent the eigenstates of H corresponding to λmax and λmin. Researchers further explored the resilience of these Dicke superposition probes to various noise models, including phase-damping, amplitude-damping, and global depolarizing noise.

This analysis revealed that certain Dicke superpositions combine super-Heisenberg scaling with improved resistance to phase damping, surpassing the performance of Fisher information optimal probes. This innovative approach establishes tailored Dicke-state superposition probes as robust resources for high-precision phase sensing in noisy quantum systems.

Dicke states demonstrate enhanced phase estimation and noise resilience in quantum sensing applications

Scientists investigated Dicke state superposition probes for phase estimation under noise, focusing on parameter encoding generated by both one- and two-body interaction Hamiltonians. The research identified a class of N-qubit Dicke superposition states exhibiting near-Heisenberg scaling of the Fisher information, alongside significantly enhanced robustness to dephasing noise when compared to GHZ, W-superposition, and balanced Dicke states, all under unitary encodings from one-body interactions.

Measurements confirm these states maintain performance advantages even with increased noise levels. For two-body interactions, the team identified Dicke superposition probes that optimize the quantum Fisher information, subsequently exploring their performance under phase-damping, amplitude-damping, and global depolarizing noise.

Tests prove that certain Dicke superpositions combine super-Heisenberg scaling with improved resilience to phase damping relative to Fisher information optimal probes. Data shows these tailored probes offer versatile and noise-resilient resources for Heisenberg and super-Heisenberg quantum phase sensing.

Experiments revealed the scaling of the quantum Fisher information and noise robustness of these Dicke superpositions, establishing their metrological utility in noisy environments. The study quantified multipartite quantum correlations within the superpositions, demonstrating their persistence even when entanglement is suppressed by noise.

Results demonstrate that these states are readily accessible multipartite resources in state-of-the-art platforms, motivating their systematic investigation in noisy settings. The work establishes that the achievable precision in parameter estimation is bounded by the quantum Cramér-Rao bound, defined by the quantum Fisher information.

Scientists calculated the classical Fisher information using probability distributions obtained from POVM measurements on the encoded states, maximizing this value to determine the QFI. Measurements confirm the QFI can be expressed as the trace of the encoded state multiplied by the square of the symmetric logarithmic derivative operator, providing a precise metric for quantum precision.

Dicke state probes optimise phase sensing with noise resilience by leveraging quantum entanglement

Scientists have identified tailored Dicke-state superposition probes as versatile resources for high-precision phase sensing. This research investigates these probes for phase estimation, considering both one- and two-body interaction Hamiltonians, and demonstrates their potential for achieving Heisenberg and super-Heisenberg scaling of the Fisher information.

A key finding is that specific Dicke superposition states exhibit near-Heisenberg scaling alongside enhanced robustness to dephasing noise, outperforming GHZ, W-superposition, and balanced Dicke states under unitary encodings. For two-body interactions, the researchers identified probes optimising the Fisher information and analysed their performance under various noise conditions, including phase-damping, amplitude-damping, and global depolarizing noise.

Certain Dicke superpositions were found to combine super-Heisenberg scaling with improved resilience to phase damping, even relative to probes already optimised for Fisher information. While optimal probes maximise quantum Fisher information in ideal conditions, they can be fragile under noise, particularly local phase damping.

Conversely, the near-optimal Dicke superposition probes demonstrated comparable, and in some instances superior, noise resilience. The authors acknowledge a limitation in that their analysis focuses on specific two-body Hamiltonians, and further work could explore a wider range of interaction types. They also note awareness of related research utilising symmetric Dicke states, highlighting that their work differs in scope by providing a unified analysis across both linear and two-body metrological schemes, with a particular emphasis on noise resilience. Future research may build on these findings to develop even more robust and efficient quantum sensors for diverse applications.