Quantum sensing is a major branch of quantum information technology that uses the principles of quantum mechanics to achieve enhanced precision and accuracy for parameter estimation and hypothesis testing problems. This paper presents a Gaussian quantum states-based quantum sensing paradigm. Gaussian quantum states have the advantage of being relatively easy to generate and manipulate in practice, and they can be used for realizing quantum sensors in the near term. Squeezed quantum states which are an example of Gaussian quantum states can improve the estimation accuracy by reducing the quantum shot noise in one of the quadratures. We present two prototypical examples of Gaussian states-based quantum sensing applications, including quadrature estimation and channel transmittance estimation of a lossy bosonic Gaussian channel. We show that improved estimation can be achieved for both problems by using squeezed states compared to classical coherent states.
Quantum sensing is a major branch of quantum information technology that uses the principles of quantum mechanics to achieve enhanced precision and accuracy for parameter estimation and hypothesis testing problems. This paper presents a Gaussian quantum states-based quantum sensing paradigm. Gaussian quantum states have the advantage of being relatively easy to generate and manipulate in practice, and they can be used for realizing quantum sensors in the near term. Squeezed quantum states which are an example of Gaussian quantum states can improve the estimation accuracy by reducing the quantum shot noise in one of the quadratures. We present two prototypical examples of Gaussian states-based quantum sensing applications, including quadrature estimation and channel transmittance estimation of a lossy bosonic Gaussian channel. We show that improved estimation can be achieved for both problems by using squeezed states compared to classical coherent states.
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.
Distributed quantum sensing has important applications in quantum-enhanced estimation of global parameters, which is the weighted sum of each sensor. Towards applications, it is essential to estimate more global parameters simultaneously. Here, we propose an improved quantum-enhanced distributed multi-parameter sensing of more than two global parameters simultaneously via Gaussian multipartite entanglement. We show that two global parameters, containing the real and imaginary parts of the complex amplitudes of multiple radio-frequency fields, can be estimated based on an Einstein-Podolsky-Rosen entangled state. Compared to the distributed quantum sensing with squeezed light in the same sensing network, the sensors are extended from M to 2 M in the improved scheme with multipartite entanglement. This work provides a practical approach for advancing high-precision multi-parameter quantum sensing technologies.
In this thesis we focus on Gaussian quantum metrology in the phase-space formalism and its applications in quantum sensing and the estimation of space-time parameters. We derive new formulae for the optimal estimation of multiple parameters encoded into Gaussian states. We discuss the discontinuous behavior of the figure of merit - the quantum Fisher information. Using derived expressions we devise a practical method of finding optimal probe states for the estimation of Gaussian channels and we illustrate this method on several examples. We show that the temperature of a probe state affects the estimation generically and always appears in the form of four multiplicative factors. We also discuss how well squeezed thermal states perform in the estimation of space-time parameters. Finally we study how the estimation precision changes when two parties exchanging a quantum state with the encoded parameter do not share a reference frame. We show that using a quantum reference frame could counter this effect.
Squeezed light, a prominent non-classical state of light, exhibits reduced quantum noise in one quadrature component below the standard quantum limit (SQL). The property enables quantum-enhanced precision measurements, surpassing the SQL in quantum sensing applications. This review comprehensively introduces the fundamental concepts, classifications, and experimental generation techniques of squeezed light. It further explores its pivotal role and recent advances in diverse quantum sensing domains, including interferometry, gravitational wave detection, magnetometry, force sensing, biomedical sensing, and quantum radar. The review covers theoretical foundations of squeezed states (including quadrature operators and classification schemes, experimental generation techniques in atomic ensembles, nonlinear crystals, and fibers), fundamentals of quantum sensing with squeezed light (from quantum noise theory to quantum-enhanced metrology), and quantum-enhanced sensing applications across the aforementioned domains. Finally, future challenges and opportunities in the field are discussed.
Bayesian quantum estimation provides a robust formalism for quantum technologies, particularly in scenarios with limited data and minimal prior information. Yet, its application to continuous-variable systems has remained limited and largely numerical due to the difficulty of the underlying parameter integrals. Here, we introduce a variational framework that restricts the optimisation over all measurements and estimators to a finite-dimensional subspace, reducing the problem to a linear system of equations with closed-form solutions. These solutions have a geometric interpretation as orthogonal projections of the global optimum onto the chosen subspace. For Gaussian states, a natural subspace is spanned by operators polynomial in the canonical quadratures, whose moments are computable from the first and second moments of the state. We further derive a necessary and sufficient condition for global optimality, and show that post-processing with the posterior mean, rather than using the estimator obtained from the subspace, improves performance towards the global optimum. Through single-shot examples, we show that the framework yields experimentally feasible strategies based on Gaussian operations and quadrature measurements that are either optimal or near-optimal.
Abstract Quantum phase estimation based on Gaussian states plays a crucial role in many application fields. In this paper, we study the precision bound for the scheme using two-mode squeezed Gaussian states. The quantum Fisher information is calculated and its maximization is used to determine the optimal parameters. We find that two single-mode squeezed vacuum states are the optimal Gaussian inputs for a fixed two-mode squeezing process. The corresponding precision bound is sub-Heisenberg-limited and scales as N −1/2. For practical purposes, we consider the effects originating from photon loss. The precision bound can still outperform the shot-noise limit when the lossy rate is below 0.4. Our work may demonstrate a significant and promising step towards practical quantum metrology.