Bosonic Diffusive Channel: Quantum Metrology via Finite Non-Gaussian Resource

TL;DR

Problem: estimate the dephasing-induced decoherence rate κ_d in a bosonic diffusive channel for continuous-variable probes. Approach: use a purification-based framework via opto-mechanical interaction to compute quantum Fisher information and compare non-Gaussian probes; key results show F_Q is proportional to ⟨n^2⟩, with non-Gaussian states such as SSKitten and SqCat providing metrological advantages at finite energy and compass-like states offering benefits in certain regimes. Ancilla-assisted readout schemes enable practical measurement when cavity fields are inaccessible, including Wigner-function reconstruction and marginal distributions. Significance: demonstrates a finite-energy route to surpass the shot-noise limit in decoherence metrology and provides design principles for probing and measuring dephasing in experimental platforms like superconducting circuits and trapped ions.

Abstract

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.

Figures (4)

• Figure 1: (Color online) The qualitative illustration of the dephasing channel via phase space diffusion of Gaussian and non-Gaussian states, when initialized in the cavity, subjected to the same dephasing induced-decoherence. The phase-space distribution ($W[\beta$]) for coherent state $\left(\ket{\alpha}\right)$ (Upper Row), squeezed state $\left(\ket{\zeta}\right)$ (Middle Row), and cat state $\left(\ket{\alpha}+\ket{-\alpha}\right)\,$(Lower Row) are shown for increasing decoherence time ($t$), leading to the symmetrical distribution around origin along phase ($\theta$).
• Figure 2: (Color online) Illustration of the dephasing-induced decoherence channel under purification via single-mode bath interactions, specifically opto-mechanical coupling. An alternative form of bath interaction can also be considered for purification or generalized modeling by incorporating the spectral response of the bath to the system via virtual bath excitation, thereby capturing diffusion-induced decoherence.
• Figure 3: (Color online) Obtained Fisher information $\langle\hat{n}^{2}\rangle$ vs. average energy $\langle\hat{n}\rangle$ of non-Gaussian probes for quantum diffusive channel when purified via single-mode opto-mechanical type interactions, considering the mechanical bath is initialized at vacuum. The symmetric squeezed compass state (SSKitten) performs well in the regime of small energy $0<\langle\hat{n}\rangle<1.5$ as compared to the other considered non-Gaussian probes: cubic phase state (CbPhS), squeezed cat state (SqCat), and symmetric squeezed state (SS).
• Figure 4: Quantum Fisher Information (QFI) obtained numerically via the symmetric logarithmic derivative (SLD) operator $\hat{L}$, plotted against the average photon number $\langle \hat{n} \rangle$ for a dephasing channel. The non-Gaussian probe states—SSKitten and SqCat—demonstrate superior performance for local estimation in the low average energy regime, while the SS yields higher QFI at large dephasing rates, indicating stronger global sensitivity. These results underscore the advantage of non-Gaussian pure probes, which offer metrological gains comparable to or exceeding those of Gaussian states, but at finite energy cost.