Optical Parametric Amplification Enables Robust Multi-Phase Estimation of Continuous Variable States

Precise parameter estimation represents a fundamental challenge across many scientific disciplines, and achieving sensitivities beyond classical limits demands innovative quantum strategies. Sijin Li and Wei Wang, from The Hong Kong Polytechnic University, alongside their colleagues, now demonstrate a significant advance in continuous variable quantum metrology, tackling the longstanding problem of fragility in squeezed states. Their research establishes that parametric amplification of entangled states dramatically improves the robustness of multi-phase estimation against unavoidable real-world losses and detection inefficiencies. By employing two-mode Einstein-Podolsky-Rosen entangled states and four-mode cluster states, the team achieves a method that promises to unlock large-scale, practical applications of high-precision measurement in challenging environments.

In the continuous variable (CV) regime, squeezed states have been exploited to implement deterministic phase estimation. However, this is often restricted by the fragility of quantum states, significantly affected by loss or detection inefficiency, which restricts its applications. This issue can be solved by using a method of parametric amplification of squeezed states, and this work implements multi-phase estimation with optical parametric amplification.

Loss-Resilient Phase Estimation with Entangled States

This research investigates methods to improve the precision of multi-parameter estimation, specifically phase estimation, using continuous-variable (CV) quantum states and entangled states like EPR states and four-mode cluster states. The study focuses on enhancing the robustness of these techniques against signal loss, a significant practical challenge in quantum systems. Scientists demonstrate that Optical Parametric Amplification (OPA) can mitigate the effects of loss and maintain enhanced precision beyond the standard quantum limit. The research utilizes CV states, described by continuous variables like the amplitude and phase of light, offering a different approach than qubit-based quantum computing.

Entanglement, a key resource for quantum enhancement, is explored through EPR states, a basic form of entanglement between two modes of light, and four-mode cluster states, a more complex multi-partite entangled state offering potential advantages for multi-parameter estimation. OPA is employed to amplify quantum signals and counteract the effects of loss, which reduces signal strength and degrades entanglement, restoring the quantum advantage. The central theme is loss tolerance, acknowledging that real-world quantum systems are imperfect and experience photon loss. Results demonstrate that OPA makes quantum-enhanced measurements more resilient to these losses, and the research extends to estimating multiple phases simultaneously, a more challenging task than single-phase estimation.

Analyses also consider asymmetric loss, where loss is not uniform across all modes of the entangled state, providing insights for optimizing the system under varying loss profiles. Specific results show that OPA consistently improves estimation sensitivity compared to scenarios without OPA and the standard quantum limit, with an optimal gain point beyond which sensitivity does not improve. The asymmetric structure of the cluster state leads to different estimation sensitivities in each mode. This research has implications for quantum sensing, improving the sensitivity of sensors for physical quantities like magnetic fields and gravitational waves, as well as for quantum metrology, enhancing the precision of measurements in general. It also benefits quantum communication and imaging, improving performance and resolution respectively. Ultimately, this work provides a theoretical framework and simulation results for building more practical and robust quantum sensors and metrology devices by combining entanglement, OPA, and loss mitigation strategies.

Entanglement Boosts Robust Multi-Phase Estimation

Scientists have achieved robust multi-phase estimation by exploiting optical parametric amplification of squeezed states, demonstrating a method resilient to signal loss and detection inefficiencies. The work centers on utilizing entanglement, specifically two-mode Einstein-Podolsky-Rosen states and four-mode cluster states, to enhance the precision of phase measurements, paving the way for large-scale applications in challenging real-world conditions. Experiments reveal that employing parametric amplification maintains sensitivity even with losses reaching 95%, a significant improvement over traditional methods where sensitivity rapidly degrades under similar conditions. The team measured phase estimation sensitivity using squeezed states with an initial squeezing of 8 dB, and found that with three stages of optical parametric amplification, the system maintains consistent performance despite substantial loss.

Data shows that the achieved sensitivity, even with amplification, surpasses the standard quantum limit in almost all loss scenarios, confirming a clear quantum advantage. Extending this approach, researchers implemented a four-mode cluster state, generating quantum correlations through beam splitters and offline squeezed states. This cluster state, when combined with optical parametric amplification, enables the estimation of four unknown phases simultaneously. Measurements confirm that the sensitivity of phase estimation remains remarkably stable under 90% loss when using the four-mode cluster state and amplification.

Calculations demonstrate that the sensitivity for estimating each of the four phases, derived from the quantum correlations within the cluster, exhibits similar resilience to loss. Specifically, the sensitivity for phase 1 shows minimal degradation and is significantly better than the standard quantum limit and the performance of a system without optical parametric amplification. This breakthrough delivers a loss-tolerant method for phase estimation, with the potential to advance technologies reliant on precise measurements in noisy environments.

Squeezed Light Amplification Boosts Phase Estimation

Scientists have developed a new method for multi-phase estimation that utilizes optical parametric amplification of entangled states generated from squeezed light, achieving sensitivity beyond classical limits. The team demonstrated that amplifying squeezed states with this technique creates a robust estimation process, significantly mitigating the detrimental effects of signal loss or imperfect detection. Analyses using both two-mode Einstein-Podolsky-Rosen entangled states and four-mode cluster states confirm the effectiveness of this approach in maintaining precision even under challenging conditions. This research establishes a pathway towards practical, large-scale quantum metrology, particularly in real-world applications where signal loss is unavoidable. The findings demonstrate that the use of optical parametric amplification effectively counteracts the degradation of estimation sensitivity caused by loss, maintaining performance levels exceeding the standard quantum limit. While the current work focuses on specific entangled states, the authors suggest that future research could explore the application of this method to more complex systems and investigate its potential for enhancing a wider range of quantum sensing technologies.