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arXiv:2601.23043 · Physical Review A

Dicke superposition probes for noise-resilient Heisenberg and super-Heisenberg Metrology

Sudha, B. N. Karthik, K. S. Akhilesh, A. R. Usha Devi

quant-phSubmitted Jan 30, 2026• Announced Feb 2, 2026• 0 citations• Revised Sep 2, 2026 (v4)
v1 · Jan 30, 2026v2 · Feb 3, 2026v3 · Jun 29, 2026v4 · Sep 2, 2026
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Abstract

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.

Journal reference
Phys. Rev. A 114, 032615 (2026)
DOI
10.1103/yk29-vcb8
Comments
15 pages, 23 figures, Accepted for publication in Physical Review A

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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.