Cubic phase states provide the essential non-Gaussian resource for continuous-variable quantum computing. We show that they also offer significant potential for quantum metrology, surpassing the phase-sensing sensitivity of all Gaussian states at equal average photon number. Optimal sensitivity requires only moderate initial squeezing, and the non-Gaussian advantage remains robust against loss and detection noise. We identify optimal measurement strategies and show that several experimentally relevant preparation schemes surpass Gaussian limits, in some cases reaching the sensitivity of cubic phase states. Our results establish cubic phase states as a promising resource for quantum-enhanced precision measurements beyond Gaussian limits.
Cubic phase states provide the essential non-Gaussian resource for continuous-variable quantum computing. We show that they also offer significant potential for quantum metrology, surpassing the phase-sensing sensitivity of all Gaussian states at equal average photon number. Optimal sensitivity requires only moderate initial squeezing, and the non-Gaussian advantage remains robust against loss and detection noise. We identify optimal measurement strategies and show that several experimentally relevant preparation schemes surpass Gaussian limits, in some cases reaching the sensitivity of cubic phase states. Our results establish cubic phase states as a promising resource for quantum-enhanced precision measurements beyond Gaussian limits.
In continuous-variable systems, non-Gaussian resources are essential for achieving universal quantum computation that lies beyond classical simulation. Among the candidate states, the cubic phase state stands out as the simplest form of single-mode non-Gaussian resource, yet its experimental preparation still remains a great challenge. Although a variety of approximate schemes have been proposed to simulate the cubic phase state, they often fall short when deployed in concrete quantum tasks. In this work, we present a Gaussian optimization protocol that systematically refines the non-Gaussian resources, which significantly improves the performance of both magic-state-based and measurement-based quantum computation. Leveraging task-specific Gaussian operations on approximate cubic phase states, our protocol offers an experimentally feasible approach to enhance gate fidelity in magic-state-based quantum computation and reduce the variance of nonlinear quadrature measurement in measurement-based quantum computation. Building on this framework, we further propose a task-oriented non-Gaussian state preparation scheme based on superpositions in the Fock basis followed by squeezing and displacement. This strategy enables direct tailoring of resource states to specific task goals. Owing to its flexibility and generality, our framework provides a powerful and broadly applicable tool for enhancing performance across a wide range of continuous-variable quantum information protocols.
Squeezed vacuum lets gravitational-wave detectors and other quantum sensors surpass the standard quantum limit, and is optimal in the loss-limited regime; phase noise breaks this optimality. Numerically optimizing the quantum Fisher information across the loss and phase-noise landscape, we identify non-Gaussian states that outperform any Gaussian state. These fall into three classes: Fock-like, cubic-phase-like, and states with discrete rotational symmetry. Limiting the average number of photons in the input state to nˉ=5, with 1−η=5% photon loss and 200 mrad phase noise, the non-Gaussian advantage reaches up to 2.2 dB. Furthermore, we observe that the non-Gaussian advantage can persist even when the measurement strategy is homodyne detection.
Quantum correlations can be harnessed to improve the precision in parameter estimation beyond classical capabilities. Under a standard interferometric or rotation protocol, it is well established that the optimal single-mode Gaussian state is a standard squeezed vacuum, which enables Heisenberg limited precision. In this work, we investigate the potential metrological advantage of two distinct families involving high-order squeezing, namely, mth-phase and multisqueezed states. Our results show that these non-Gaussian states can grant a significant metrological advantage with respect to the optimal squeezed vacuum under equivalent conditions, i.e. at equal occupations. Their advantage holds both at low and large occupations, but its behavior critically depends on the chosen family of high-order squeezing. While higher squeezing orders enhance the advantage, this comes at the cost of higher-order observables in the measurement for full metrological performance. Finally, we study their robustness to standard decoherence channels, i.e. pure dephasing and zero-temperature damping. Employing standard squeezing as reference state, our results indicate a reasonable robustness against damping up to a certain noise strength, while their metrological advantage becomes fragile under pure dephasing. Our work shows the potential enhancement in quantum metrology beyond Gaussian states, carefully detailing the main challenges and limitations.
Quantum metrology aims to achieve measurement precision that surpasses classical limits in the estimation of physical parameters. In realistic conditions, however, its advantage can be diminished by interactions between a quantum system and its environment. This necessitates careful design of quantum resources that can sustain enhanced performance even under noise. Here, we investigate how a quantum non-Gaussian operation can provide an advantage in noisy quantum metrology. Specifically, we examine the effect of single-photon subtraction applied to a two-mode squeezed vacuum state in the task of phase estimation using a Mach–Zehnder interferometer under photon loss. The single-photon subtraction can be implemented either before or after the first beam splitter in the interferometer. By evaluating the quantum Fisher information for both the original and the photon-subtracted states, we assess the potential enhancement in sensing precision. We show that the enhancement occurs when photon subtraction is performed before the first beam splitter, provided that loss acts only on the signal mode. Our findings shed light on the role of non-Gaussian operations in noisy quantum metrology, clarifying when photon subtraction can yield a genuine advantage over Gaussian resources.
As one of the main pillars of quantum technologies, quantum metrology aims to improve measurement precision using techniques from quantum information. The two main strategies to achieve this are the preparation of nonclassical states and the design of optimized measurement observables. We discuss precision limits and optimal strategies in quantum metrology and sensing with a single mode of quantum continuous variables. We focus on the practically most relevant cases of estimating displacements and rotations and provide the sensitivities of the most important classes of states that includes Gaussian states and superpositions of Fock states or coherent states. Fundamental precision limits that are obtained from the quantum Fisher information are compared to the precision of a simple moment-based estimation strategy based on the data obtained from possibly sub-optimal measurement observables, including homodyne, photon number, parity and higher moments. Finally, we summarize some of the main experimental achievements and present emerging platforms for continuous-variable sensing. These results are of particular interest for experiments with quantum light, trapped ions, mechanical oscillators, and microwave resonators.
As a cornerstone of quantum science and technology, quantum precision measurement aims to transcend the standard quantum limit (SQL) and achieve sensitivities unattainable by classical approaches by harnessing distinctive quantum resources such as entanglement, squeezing and non-Gaussianity. Within this framework, Gaussian states have historically played a central role, underpinning a series of seminal experimental advances; however, their utility in metrology is fundamentally bounded by theoretical constraints that preclude unlimited gains in measurement precision. In contrast, a growing body of recent research has revealed that non-Gaussian states–endowed with stronger quantum correlations and more pronounced non-classical characteristics — can significantly surpass Gaussian counterparts in key tasks such as phase estimation, quantum imaging and quantum sensing. Under specific conditions, these states even exhibit the potential to approach or saturate the ultimate Heisenberg limit. This review offers a comprehensive overview of the theoretical underpinnings, representative preparation methodologies, experimental progress and emerging applications of non-Gaussian states in quantum metrology. Special attention is devoted to illustrating their transformative potential for the development of next-generation quantum sensors and high-precision measurement instruments, while also addressing prevailing challenges and delineating promising future research trajectories in this rapidly advancing field.