Abstract Leveraging the unique quantum properties of non-Gaussian states is crucial for advancing continuous variable quantum technologies. Recent experimental advancements in generating non-Gaussian states, coupled with theoretical findings of their superior performance in quantum information protocols compared to Gaussian states, motivate this investigation. This work investigates the role of the non-Gaussianity on the frequency estimation problem. The analysis focuses on a single bosonic mode and its non-Gaussian excited states as probe states, while the frequency estimation is investigated by explicitly computing the quantum Fisher information. Firstly, we consider a stationary regime, where the study of single Fock states yields a deeper understanding of the behavior of the non-Gaussianity as well as its comparison with other relevant candidates to probes, such as the coherent and squeezed vacuum states. Here, the connection with the non-Gaussianity is also discussed, as well as the Heisenberg limit and the comparison with other relevant superposition states for the same task. The results indicate that the advantage in using Fock states as probes for frequency estimation is directly associated with the degree of non-Gaussianity of the probe.
Abstract Leveraging the unique quantum properties of non-Gaussian states is crucial for advancing continuous variable quantum technologies. Recent experimental advancements in generating non-Gaussian states, coupled with theoretical findings of their superior performance in quantum information protocols compared to Gaussian states, motivate this investigation. This work investigates the role of the non-Gaussianity on the frequency estimation problem. The analysis focuses on a single bosonic mode and its non-Gaussian excited states as probe states, while the frequency estimation is investigated by explicitly computing the quantum Fisher information. Firstly, we consider a stationary regime, where the study of single Fock states yields a deeper understanding of the behavior of the non-Gaussianity as well as its comparison with other relevant candidates to probes, such as the coherent and squeezed vacuum states. Here, the connection with the non-Gaussianity is also discussed, as well as the Heisenberg limit and the comparison with other relevant superposition states for the same task. The results indicate that the advantage in using Fock states as probes for frequency estimation is directly associated with the degree of non-Gaussianity of the probe.
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.
The fundamental metrological limits of temperature sensing in open quantum systems remain largely unresolved, particularly regarding the role of non-Gaussian quantum resources. In this letter, we establish analytic bounds on the quantum Fisher information (QFI) for temperature estimation using non-Gaussian states undergoing dissipative bosonic evolution. By focusing on the short-time regime governed by a time-local master equation, we derive precise scaling laws that elucidate when and how non-Gaussian probes decisively outperform Gaussian states under identical energy constraints. Our analysis uncovers a distinct linear-in-time QFI enhancement unique to Fock states, in contrast to the inherently weaker, quadratic scaling of Gaussian probes. These theoretical insights are substantiated through exact numerical simulations and mapped onto experimentally accessible platforms such as circuit QED. Our results not only clarify the quantum thermometric advantage of non-Gaussianity but also chart a realistic pathway toward harnessing it in noisy quantum technologies.
Gaussian quantum states and channels are pivotal across many branches of quantum science and their applications, including the processing and storage of quantum information, the investigation of thermodynamics in the quantum regime, and quantum computation. The great advantage is that Gaussian states are experimentally accessible via their first and second statistical moments. In this work, we investigate parameter estimation for Gaussian states, in which the probe-state preparation stage involves two noncommutative Gaussian measurements on the position and momentum observables, introducing tunable parameters. The influence of these noncommutative Gaussian measurements is investigated through the quantum Fisher information (QFI). We showed that the QFI for characterizing Gaussian channels can be increased by adjusting the uncertainty parameters in the preparation of the probe state. Furthermore, if the probe is initially in a thermal state, probe-state preparation may generate quantum coherence in its energy basis. We showed that not only does the amount of coherence affect the improvement of the QFI, but also the rate of change of the coherence with respect to the parameter to be estimated. The proposed probe-state protocol is applied to two paradigmatic single-mode Gaussian channels, the attenuator and amplification channels, which are building blocks of Gaussian quantum information. Our results contribute to the use of coherence in quantum metrology and are experimentally feasible in quantum-optical devices.
Abstract We study the estimation precision attainable by entanglement-enhanced Ramsey interferometry in the presence of spatiotemporally correlated non-classical noise. Our analysis relies on an exact expression of the reduced density matrix of the qubit probes under general zero-mean Gaussian stationary dephasing, which is established through cumulant-expansion techniques and may be of independent interest in the context of non-Markovian open dynamics. By continuing and expanding our previous work (Beaudoin et al 2018 Phys. Rev. A 98 020102(R)), we analyze the effects of a non-collective coupling regime between the qubit probes and their environment, focusing on two limiting scenarios where the couplings may take only two or a continuum of possible values. In the paradigmatic case of spin–boson dephasing noise from a thermal environment, we find that it is in principle possible to suppress, on average, the effect of spatial correlations by randomizing the location of the probes, as long as enough configurations are sampled where noise correlations are negative. As a result, superclassical precision scaling is asymptotically restored for initial entangled states, including experimentally accessible one-axis spin-squeezed states.
Quantum non-Gaussian states of photons and phonons are conclusive and direct witnesses of higher-than-quadratic nonlinearities in optical and mechanical processes. Moreover, they are proven resources for quantum sensing, communication and error correction with diverse continuous-variable systems. This review introduces theoretical analyses of nonclassical and quantum non-Gaussian states of photons and phonons. It recapitulates approaches used to derive operational criteria for photons tolerant to optical losses, their application in experiments and their nowadays extension to quantum non-Gaussian photon coincidences. It extends to a recent comparison of quantum non-Gaussianity, including robustness to thermal noise, and sensing capability for high-quality phononic Fock states of single trapped cooled ions. The review can stimulate further development in the criteria of quantum non-Gaussian states and experimental effort to prepare and detect such useful features, navigating the community to advanced quantum physics and technology.
Subject of study. Schemes for generating non-Gaussian quantum states and the states required for quantum error correction protocols are investigated. Aim of study. The primary objectives were to generalize methods and approaches for describing the generation of non-Gaussian states in measurement schemes to determine the most effective model for describing the generation process and to assess a model for generating squeezed Fock states and a quantum error correction code based on such states. Method. A theoretical analysis of the wavefunction evolution of various non-Gaussian states in particle-number measurement schemes was performed; in this analysis, squeezed states were used as inputs. Main results. A scheme for generating squeezed Fock states was theoretically examined. An explicit analytical expression for the output wavefunction was constructed to completely analyze the output states depending on the parameters of the scheme under consideration. A set of conditions imposed on the parameters of a two-mode entangled Gaussian state, i.e., the “universal solution regime,” was outlined. This regime guaranteed the generation of squeezed Fock states with a high probability. Practical significance. The results demonstrated the ability of the universal solution regime to generate squeezed Fock states of arbitrary order for a given squeezing parameter. The feasibility of using squeezed Fock states in quantum error correction codes was analyzed. A comparative study of squeezed Fock states and squeezed Schrödinger cat states as codewords confirmed squeezed Fock states as robust solutions to ensure information protection in channels subjected to particle loss and dephasing.