We investigate the estimation of dephasing-induced decoherence in continuous-variable quantum systems using non-Gaussian probe states. By purifying the open system, we identify optimal probes, specifically squeezed cat and symmetric squeezed compass states, via quantum Fisher information. These results are in agreement with numerical simulation. In settings where the intra-cavity field is inaccessible and standard measurements are impractical, utilizing an ancilla approach where a qubit traverses or interacts with the cavity field, leading to measurement of the qubit, hence allowing estimation of the dephasing rate via Wigner function reconstruction or less costly marginal distribution.
We investigate the estimation of dephasing-induced decoherence in continuous-variable quantum systems using non-Gaussian probe states. By purifying the open system, we identify optimal probes, specifically squeezed cat and symmetric squeezed compass states, via quantum Fisher information. These results are in agreement with numerical simulation. In settings where the intra-cavity field is inaccessible and standard measurements are impractical, utilizing an ancilla approach where a qubit traverses or interacts with the cavity field, leading to measurement of the qubit, hence allowing estimation of the dephasing rate via Wigner function reconstruction or less costly marginal distribution.
Gaussian quantum channels are relevant operations in continuous variable systems. In general, given an arbitrary state, the action on it is well known, provided that the quantum channels are completely characterized. In this work, we have studied the role played by quantum coherence in the estimation of Gaussian channel parameters. For this purpose, we start by considering an initial single-mode vacuum state where coherence is generated through displaced or/and squeezing operations. Then, we consider a probe state with two resources, the average thermal number and the quantum coherence. The results are computed using the quantum Fisher information (QFI) as well as some gain functions defined in the work. We applied the estimation protocol for two paradigmatic bosonic Gaussian channels: the thermal attenuator and the thermal amplifier. Our results show that for the vacuum initial state, coherence can be exploited to obtain a high QFI. Moreover, we can state two important facts: the first being that for a small parameter region of a channel, the QFI depends on the mechanism used to generate the coherence, while the second is that the QFI depends not only on the amount of coherence but also on how it changes as a function of the parameter to be estimated. For the probe state, including also an average thermal number, the two examples show that thermal resources are not always beneficial to the QFI and that this depends on the channel structure. For the attenuator channel, the optimal probe state is only limited by the ability to implement an average thermal number and generate an amount of coherence, while for the amplifier channel, the vacuum probe state with coherence is the optimal state. Finally, we obtain a direct relation between the quantum Fisher information and the relative entropy of coherence, allowing, in principle, an experimental verification based on the measurement of the covariance matrix of the probe system.
We investigate the optimal estimation of dephasing in finite-dimensional quantum spin systems. We first discuss some properties of the optimal probe states and present an efficient numerical algorithm to compute the optimal precision in dephasing estimation and identify the optimal probe states. For the dephasing channel arising from Gaussian phase diffusion, a spin cat state is known to be optimal for small dephasing. We analytically determine the range of dephasing strengths over which the cat state remains globally optimal for spins J=1 and J=3/2, and derive upper bounds on its optimality region for larger spins. We then compare numerically several probe states proposed in the literature, showing in particular that the simple class of probes obtained from uniform superpositions of all levels performs near-optimally for stronger dephasing. Finally, we apply our framework to a central-spin model coupled to a nuclear-spin bath, whose dynamics we simulate using the cluster-correlation expansion. Our results show that, while the cat state is optimal for weak Gaussian dephasing, pulse-controlled non-Markovian dynamics can favor states with amplitudes distributed over multiple spin levels, and in some cases the uniform state outperforms the other fixed probes considered. This shows how the choice of probe state depends both on the dephasing strength and on the dynamics.
Non-Gaussian bosonic states are ubiquitous in interacting light--matter systems, many-body platforms, and relativistic quantum field settings, but their quantitative characterization is hindered by the infinite-dimensional Hilbert space and by the poor scalability of Fock-space truncation methods. We introduce an exact finite-manifold encoding for states supported on a finite span of Gaussian branches, enabling the use of standard finite-dimensional quantum-information tools directly on an effective density matrix whose entries are determined by Gaussian overlaps. As demonstrations, we obtain closed-form and numerically stable evaluations of entropies and relative-entropy non-Gaussianity, and derive an analytic expression for the bipartite entanglement negativity of arbitrary multimode two-branch Gaussian superpositions, including a minimal which-branch dephasing model. Our framework provides a practical bridge between experimentally accessible continuous-variable resources (e.g., cat-like and measurement-conditioned states) and discrete-variable information measures, with immediate applications to benchmarking non-Gaussian resources in several quantum technology platforms.
Deterministic preparation of bosonic resource states is a central task in continuous-variable quantum information processing and quantum metrology. Here we develop a measurement-based imaginary time evolution (MITE) protocol for preparing squeezed and non-Gaussian states. The protocol combines ancilla-mediated weak measurements of the Hamiltonian with a conditional phase rotation that suppresses excited state trapping and stabilizes convergence toward the ground state. The method is potentially applicable in hybrid discrete variable-continuous variable (DV-CV) platforms, where the qubit acts as the measurement readout. We demonstrate deterministic convergence over a broad range of parameters and show that the performance degradation near the stability boundary is governed by the shrinking Bogoliubov quasiparticle gap. The same framework also extends to non-Gaussian bosonic resource states, including Schrödinger cat states and excited states of the single-mode squeezing Hamiltonian, which display Wigner negativity. The squeezed states remain robust under bosonic loss over experimentally relevant regimes.
Quantum metrology enables sensitivity to approach the limits set by fundamental physical laws. Even a single continuous mode offers enhanced precision, with the improvement scaling with its occupation number. Due to their high information capacity, continuous modes allow for the engineering of quantum non-Gaussian states, which not only improve metrological performance but can also be tailored to specific experimental platforms and conditions. Recent advancements in control over continuous platforms operating in the quantum regime have renewed interest in sensing weak forces, also coupling to massive macroscopic objects. In this work, we investigate a force-sensing scheme where a physical process completely randomizes the direction of the induced phase-space displacement, and the unknown force strength is inferred through excitation-number-resolving measurements. We find that N-spaced states, where only every N^{th} Fock state occupation is nonzero, approach the achievable sensing bound. Additionally, non-Gaussian states are shown to be more resilient against decoherence than their Gaussian counterparts with the same occupation number. While Fock states typically offer the best protection against decoherence, we uncover a transition in the metrological landscape-revealed through a tailored decoherence-aware Fisher-information-based reward functional-where experimental constraints favor a family of number-squeezed Schrödinger cat states. Specifically, by implementing quantum optimal control in a minimal spin-boson system, we identify these states as maximizing force sensitivity under lossy dynamics and finite system controllability. Our results provide a pathway for enhancing force sensing in a variety of continuous quantum systems, ranging from massive systems like mechanical oscillators to massless systems such as quantum light and microwave resonators.
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.