Spin-squeezed states enable entanglement-enhanced frequency estimation; however, the achievable performance is limited in practice by decoherence. We study the problem of parameter estimation under \emph{classical collective noise} that acts along a \emph{fixed} direction during signal encoding. While we restrict our analysis to Gaussian noise statistics, no assumption is made on the nature of the noise temporal correlations. Our approach captures both parallel (dephasing) and single-axis transverse noise as special cases, and covers both Markovian and non-Markovian metrological regimes. In the properly squeezed limit, where a Holstein-Primakoff description is accurate, we identify a geometric noise-immunity mechanism: for \emph{known} non-parallel signal and noise axes, an appropriate one-axis-twisted input encodes the signal in a quadrature that is metric-orthogonal to the direction of noise-induced diffusion. Irrespective of the noise temporal correlations, the resulting estimation precision exhibits Heisenberg scaling in the probe number. Optimal performance is achievable by measuring a single collective spin component. Imperfect knowledge of the noise axis produces a crossover from Heisenberg scaling at moderate probe number back to the known collective-dephasing bounds asymptotically.
Preserving quantum coherence in the presence of environmental noise is one of the principal challenges for quantum technologies. Noise mitigation using spectator qubits (SQs) has recently emerged as a promising approach, enabling indirect probing of the noise without disturbing the data qubit (DQ). However, existing analyses that probe ultimate performance have been restricted to two-state random telegraph process noise, which does not capture more complex noise processes that may arise in the environment. Therefore, we here develop a SQ-based noise mitigation for DQs subject to general multi-level fluctuator noise. We first derive the coherence dynamics of the DQ under such noise, then develop a mitigation scheme in which information about the noise is inferred from sequential SQ measurements and used for phase correction. A memory-efficient heuristic adaptive protocol is proposed to dynamically select the SQ measurement time and angle based on the current noise estimate. Numerical simulations demonstrate that the proposed strategy significantly suppresses decoherence under multi-level noise, achieving performance comparable to that in the two-level case despite the increased complexity of the noise process.
Yanan Liu, Hongting Song, A. Chantasri et al.· 0 citations
Recently, it has been shown that protocols utilizing infinitely fast controls, such as quantum error correction, can in principle restore Heisenberg-limited frequency estimation in the presence of a broad class of non-Markovian noise models arising from coupling to finite-dimensional environments. However, these controls differ substantially from those used to address Markovian noise, and their underlying physical mechanism remains unclear. In this work, we establish a direct connection between these protocols and the quantum Zeno effect, and extend the framework to infinite-dimensional environments. We delineate three types of constructions: (a) protocols that rely solely on measurements, (b) protocols using an active recovery after measurements and (c) protocols using dynamical decoupling and rigorously analyze the performance of each when controls can be applied at only a finite rate. While protocols relying purely on measurements can be engineered for noise models where active recoveries are fundamentally impossible, they result in the quantum Fisher information exhibiting a quadratically worse dependence on the control frequency. Surprisingly, while dynamical decoupling protocols are possible whenever protocols relying only on measurements can be engineered, the quantum Fisher information has the same dependence on control frequency as the active recovery protocols. Numerical simulations suggest that the improvement offered by dynamical decoupling may work in regimes beyond the perturbative setting where our rigorous theorems apply.
Randomized measurements provide an efficient way to extract physical properties of an unknown quantum state from limited data. On near-term hardware, gate and readout errors bias the reconstructed observables. Here we develop a microscopic description of this bias for locally scrambled shallow circuits. Independent local twirling reduces local implementation noise to stochastic Pauli damping, and a noise event contributes only when it overlaps the Heisenberg evolution of the measured Pauli operator. This gives an activated path-average formula for the noisy Pauli coefficient. In one-dimensional shallow circuits, the activated noise volume grows linearly with the size of a contiguous observable, leading to an exponential damping ratio. We verify this scaling for two-qubit random Clifford and locally scrambled iSWAP circuits with two-qubit Pauli noise, including spatial fluctuations and temporal drift. The scaling supports a small-string calibration protocol that predicts larger string observables without learning the full noisy measurement channel. Our result relates the noise bias of shallow-shadow protocols directly to operator-evolving dynamics.
We introduce the wavemap: a spatial portrait of noise effects that assigns each site a per-noise-level arrival delay l_\gamma (v) and cross-entropy loss L_\gamma(v). These observables are exact at the lightcone frontier, where bond dimension \chi is small and the simulation is most faithful. Eigenvalue analysis of the composed gate-plus-noise Pauli transfer matrices confirms that the studied noise is pure amplitude damping: the spatial propagation pattern is entirely determined by the gate, making the wavemap a model-free noise diagnostic. We apply the multi-product formula (MPF) to recover the noiseless Pauli weight field from the noisy samples, subject to the Lieb-Robinson causal constraint nMPF<= nnl . Fitting time-adaptive coefficients \alpha(t) over the frontier recovers up to 55% of the information loss relative to the best noisy sample, exploiting the fact that the frontier is where truncation error is smallest. On an IBM heavy-hex lattice with heterogeneous hardware noise the method identifies an information-starved regime, pointing to calibrated synthetic noise as the next required experiment.
Quantum sensors promise measurement sensitivities that can scale at the Heisenberg limit, but in practice their performance is often degraded by noise, finite sampling, and implementation imperfections. In this work we present a general framework for improving parameter estimation in such settings by exploiting intrinsic structural constraints of time-domain correlation functions. Our approach builds on the observation of Kemper et al (2024 Phys. Rev. Lett. 132 160403) that two-time correlation functions of Hermitian observables generate Gram matrices that are positive semidefinite, a property that can be violated in experimentally acquired data. We formulate signal reconstruction as a convex optimization problem that enforces positive semidefiniteness, Toeplitz structure, and low-rank priors motivated by the underlying dynamics. We show analytically that, under suitable conditions, the ground-truth signal can be uniquely identified in the noiseless case and recovered stably in the presence of noise. We further demonstrate numerically, in a Greenberger–Horne–Zeilinger-based magnetometry protocol, that enforcing these physical constraints can significantly improve frequency estimation from sparse and noisy data. In particular, we observe a clear advantage in the data-starved regime, where only a small number of time samples are available and standard spectral estimation methods, including matrix pencil techniques, provide limited or unstable improvement over direct fitting. While the reconstructed signals do not in general reach the shot-noise-limited performance, the proposed approach consistently reduces estimation error and recovers much of the underlying structure of the signal. These results indicate that incorporating universal physical constraints into data analysis can enhance the practical performance of quantum sensing protocols without requiring additional hardware resources or calibration.
Amir Kalev· Quantum Science and Technolo...· 0 citations
Real-time monitoring of weak entanglement in noisy fiber links is a practical bottleneck for entanglement-based quantum key distribution (QKD). Standard concurrence and negativity vanish with vanishing gradient near the separability boundary and are not optimized for hardware-level line-rate monitoring. We propose a closed-form, noise-robust entanglement indicator [Formula: see text] for two-qubit mixed states, constructed by regularizing the Wootters concurrence with a determinant-based spectral penalty. [Formula: see text] requires no iterative optimization, retains a nonvanishing gradient along typical QKD noise trajectories, and has an average computation time of 0.189 ms per state. Numerical simulations over 100,000 random states show strong linear correlation with negativity (Pearson 0.986) and entanglement of formation (0.968). Under 12 common LOCC channels relevant to QKD, [Formula: see text] is nonincreasing in 100% of tested cases. A field-programmable gate array (FPGA) implementation achieves 210 ns latency, enabling real-time link health monitoring in metropolitan QKD networks.
Hanha Yan· International Journal of Qua...· 0 citations
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