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arXiv:2608.18757

Robustness of spin state superpositions for noisy quantum metrology

Trinidad B. Lantaño, Gabriela Wójtowicz, Susana F. Huelga, Martin B. Plenio

quant-phSubmitted Aug 19, 2026• Announced Aug 20, 2026• 0 citations
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Abstract

Quantum metrology faces major challenges in noisy environments, where decoherence rapidly degrades useful quantum resources. We investigate the dynamics of the precision limits given by the quantum Fisher information (QFI) for phase estimation under spatially correlated dephasing. We characterize the dynamics of the QFI by the sensitivity and degradation indicators that can be obtained as analytical expressions derived using perturbative theory treatment. These short-time and weak-noise formulas yield analytic insight into how collective-spin moments govern both (i) the noiseless sensitivity and (ii) the leading noise-induced degradation of metrological usefulness. We identify a trade-off that is intrinsic to our commuting encoding-noise structure. We analyze the QFI dynamics for the Gaussian spin state (GSS) superpositions, encompassing spin coherent state (SCS), Dicke state superpositions, spin-squeezed states, and GHZ-like states. Predictions from indicators of the QFI dynamics are compared to both the quantum Cramér--Rao bound and the measurement-specific sensitivity bounds for an optimal parameter and interrogation time under a finite total time resource. When possible, we analytically derive the measurement-specific sensitivity bounds for spin-projection and parity-based measurements.

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Quantum metrology faces major challenges in noisy environments, where decoherence rapidly degrades useful quantum resources. We investigate the dynamics of the precision limits given by the quantum Fisher information (QFI) for phase estimation under spatially correlated dephasing. We characterize the dynamics of the QFI by the sensitivity and degradation indicators that can be obtained as analytical expressions derived using perturbative theory treatment. These short-time and weak-noise formulas yield analytic insight into how collective-spin moments govern both (i) the noiseless sensitivity and (ii) the leading noise-induced degradation of metrological usefulness. We identify a trade-off that is intrinsic to our commuting encoding-noise structure. We analyze the QFI dynamics for the Gaussian spin state (GSS) superpositions, encompassing spin coherent state (SCS), Dicke state superpositions, spin-squeezed states, and GHZ-like states. Predictions from indicators of the QFI dynamics are compared to both the quantum Cramér--Rao bound and the measurement-specific sensitivity bounds for an optimal parameter and interrogation time under a finite total time resource. When possible, we analytically derive the measurement-specific sensitivity bounds for spin-projection and parity-based measurements.
We present a closed-form analytical description for the metrological performance of a generic superposition of spin coherent states (SSCS) used as probes for quantum phase estimation. Working in this framework, we derive transparent analytical expressions for the pertinent quantum Fisher information and identify a general class of spin coherent states enabling quantum metrology with Heisenberg-limit precision. Bloch-sphere analysis of antipodal SSCS shows that the phase-estimation precision attainable with such states increases with the distance from the equator of the Bloch sphere, growing from the shot-noise limit level for the equatorial states all the way up to the Heisenberg limit for SSCS that can be represented as superpositions of the poles of the Bloch sphere.
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.
We derive ultimate precision bounds for estimating parameters encoded in \emph{time-dependent} Hamiltonians in the presence of general Markovian noise, allowing for arbitrary adaptive protocols with fast controls and noiseless ancillas. Extending the minimization-over-purifications framework to time-varying continuous channels, we obtain a differential upper bound on the achievable quantum Fisher information (QFI) that can be evaluated at all times via semidefinite programming. For parameter-independent noise, we prove a universal long-time scaling law: if the coherent (noiseless) dynamics yields Qcoh(T)∼T2kQ_{\mathrm{coh}}(T)\sim T^{2k}Qcoh​(T)∼T2k, then under Markovian noise the QFI scales at most as Q(T)∼T2kQ(T)\sim T^{2k}Q(T)∼T2k in the DHNLS regime, whereas in the DHLS regime it is fundamentally limited to Q(T)∼T2k−1Q(T)\sim T^{2k-1}Q(T)∼T2k−1. We illustrate these behaviors on paradigmatic driven-qubit sensors, exhibiting T4T^{4}T4 and T3T^{3}T3 scalings under dephasing and spontaneous emission, respectively. Finally, we provide explicit continuous exact and approximate quantum error correction constructions -- supplemented by spin-squeezed probes -- that asymptotically saturate the bounds, establishing their tightness.
We examine metrological scenarios where the parameter of interest is encoded onto a quantum state through the action of a noisy quantum gate and investigate the ultimate bound to precision by analyzing the behavior of the quantum Fisher information (QFI). We focus on qubit gates and consider the possibility of employing successive applications of the gate. We go beyond the trivial case of unitary gates and characterize the robustness of the metrological procedure introducing noise in the performed quantum operation, looking at how this affects the QFI at different steps (gate applications). We model the dephasing and tilting noise affecting qubit rotations as classical fluctuations governed by a von Mises--Fisher distribution. Compared to the noiseless case, in which the QFI grows quadratically with the number of steps, we observe a nonmonotonic behavior, and the appearance of a maximum in the QFI, which defines the ideal number of steps that should be performed in order to precisely characterize the action of the gate. Analyzing also the combination of different types of gate imperfections we defined a form of generic noise, finding also nontrivial regimes in which the combination of the two different noises leads to a more resilient QFI or, more remarkably, to an enhancement of the QFI with respect to the case in which only one type of noise is considered.
Quantum-enhanced interferometers utilize non-classical states of light in order to surpass the limitations imposed by classical physics on phase measurement sensitivity and resolution. We review key scientific developments in this growing field of research and derive fundamental metrology concepts, namely the Cram\'{e}r-Rao bound and the Fisher information, which are used to analyze the metrological performance of quantum states of light. We propose a supersensitive quantum interferometry protocol that can be amplified to the macroscopic realm (i.e. the mean number of photons of the probe state can reach approximately 100,000 photons) using contemporary techniques of spontaneous parametric down conversion. The parity measurement on the output field asymptotically saturates the quantum Cram\'{e}r-Rao bound, which scales like the Heisenberg limit. We uncover the role of photon statistics on phase sensitivity and rule out the necessity of mode entanglement for quantum-enhanced interferometry. Based on these insights we outline a practical metrology technique (independent of mode entanglement) that measures a phase delay of a single-mode anti-squeezing operation. This scheme can also be scaled macroscopically using contemporary techniques and is shown to significantly surpass the shot-noise limit (SNL) in the presence of realistic losses. Finally, the physical resources that enable quantum-enhanced interferometry is studied by analyzing the quantum Fisher information (QFI) using the first quantization and the second quantization formalisms of quantum mechanics. It is shown that increasing the intra-mode correlations of an interferometer (as quantified by the second order Glauber coherence function) can be conducive to attaining a quantum advantage in phase estimation; whereas, introducing mode entanglement can reduce phase sensitivity. Using the first quantization description, we derive a formula for the QFI that shows explicitly how the Heisenberg scaling term depends on particle entanglement.
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.