We investigate how squeezing techniques can improve the measurement precision in multiphase quantum metrology. While these methods are well studied and effectively used in single-phase estimations, their usage in multiphase situations has yet to be examined. We fill this gap by investigating the mechanism of quantum enhancement in the multiphase scenarios. Our analysis provides theoretical and numerical insights into the optimal condition for achieving the quantum Cramér-Rao bound, helping us understand the potential and mechanism for quantum-enhanced multiphase estimations with squeezing. In this paper, we open possibilities for advancements in quantum metrology and sensing technologies. Published by the American Physical Society 2024
We investigate how squeezing techniques can improve the measurement precision in multiphase quantum metrology. While these methods are well studied and effectively used in single-phase estimations, their usage in multiphase situations has yet to be examined. We fill this gap by investigating the mechanism of quantum enhancement in the multiphase scenarios. Our analysis provides theoretical and numerical insights into the optimal condition for achieving the quantum Cramér-Rao bound, helping us understand the potential and mechanism for quantum-enhanced multiphase estimations with squeezing. In this paper, we open possibilities for advancements in quantum metrology and sensing technologies. Published by the American Physical Society 2024
Abstract In quantum metrology, it is widely believed that the quantum Cramér–Rao bound is an attainable bound. However, this is not always true. In order to clarify this point, we explain why the quantum Cramér–Rao bound cannot be attained. Here, we investigate noiseless channel estimation under energy constraint for states, using a physically reasonable error function, and present a state achieving the optimal rate as well as the attainable bound. We propose an experimental generation of the optimal states for enhanced metrology using squeezing transformations. This makes phase/unitary estimation physically implementable.
Squeezed light enables quantum-enhanced phase estimation, with crucial applications in both fundamental physics and emerging technologies. To fully exploit the advantage provided by this approach, estimation protocols must remain optimal across the entire parameter range and resilient to instabilities in the probe state. In this context, strategies that rely on pre-calibrated squeezing levels are vulnerable to degradation over time and become sub-optimal when experimental conditions fluctuate. Here, we develop an adaptive multiparameter estimation strategy for ab-initio phase estimation, achieving sub-shot noise limit precision in the full periodicity interval [0, π), without relying on prior knowledge of the squeezing parameter. Our approach employs real-time feedback to jointly estimate both the optical phase and the squeezing level, ensuring robustness against experimental drifts and calibration errors. This self-calibrating scheme establishes a reliable quantum-enhanced sensing framework, opening new routes for practical scenarios and scalable distributed sensor networks using squeezed light.
With the rapid advancement of science and technology, phase measurement plays a crucial role in various fields such as optics, communication, and radar. Traditional phase measurement methods, relying on classical light sources, produce results following the central limit theorem, limiting measurement precision to the standard quantum limit. However, recent in-depth studies of quantum theory and quantum enhanced experimental techniques are breaking this barrier. The use of specially designed non-classical light sources for phase measurement not only provides the possibility of breaking through the limits of measurement precision but also meets the growing demand for high-precision measurements.This paper started from a statistical perspective, introduced key indicators for evaluating measurement precision, including the Cramér-Rao Boundary (CRB) and Fisher Information, and extends to experimental approaches beyond the standard quantum limit. Subsequently, by introducing quantum light sources such as squeezed states, entangled states, and methods like harmonic amplification to achieve amplifier the phase and optical detection, the paper provides a comprehensive review of recent research achievements in super-resolution phase measurement techniques. Finally, we select several technological categories with a promising engineering outlook, analyze the technical challenges limiting their maturity, and provide a prospective outlook.
High-precision quantum parameter estimation is fundamental to the advancement of quantum metrology. Although reservoir engineering provides a powerful approach to improve estimation by tailoring system-environment interactions, the role of the squeezing phase and correlations arising from the sequential utilization of the same squeezed reservoir remains inadequately explored. In this work, we employ a correlated squeezed-thermal reservoir to enhance the precision of estimating the phase parameter φ and the correlation factor μ, both individually and simultaneously. We show that the squeezing phase Φ is crucial for achieving quantum-enhanced precision, with optimal phase-matching conditions that depend strongly on μ. Specifically, we derive the near-optimal phase-matching relations aimed at maximizing the quantum Fisher information (QFI) for both φ and μ, as well as minimizing the total variance Δsim in joint estimation. Furthermore, we show that the joint estimation variance is dominated by Fφ, which motivates our search for the phase-matching conditions that minimize Δsim. Through the ratio R of variances, we demonstrate that joint estimation conserves quantum resources and maintains high precision when the squeezing phase is optimized for Fφ, despite the inherent incompatibility of the parameters. These findings provide practical insights into reservoir engineering strategies for high-precision quantum sensing and information processing.
A usual assumption in quantum estimation is that the unknown parameter labels the possible states of the system, while it influences neither the sample space of outcomes nor the measurement aimed at extracting information on the parameter itself. This assumption is crucial to prove the quantum Cram\'er-Rao theorem and to introduce the quantum Fisher information as an upper bound to the Fisher information of any possible measurement. However, there are relevant estimation problems where this assumption does not hold and an alternative approach should be developed to find the genuine ultimate bound to precision of quantum measurements. We investigate physical situations where there is an intrinsic dependence of the measurement strategy on the parameter and find that quantum-enhanced measurements may be more precise than previously thought.
Phase estimation has a wide range of applications. Over the years, several strategies have been studied to improve precision in phase estimation. These strategies include using exotic quantum states to quantum detection schemes. This dissertation summarizes my effort in improving the precision of phase estimation with a linear and nonlinear interferometer. Chapter 1 introduces quantum optics and quantum metrology. I introduce all relevant quantum states of light used. We also look into tools and terminologies of quantum metrology such as Fisher information, shot-noise limit, Heisenberg limit, etc., along with examples of phase estimation with a Mach-Zehnder interferometer. In Chapter 2, I discuss multiple phase estimation using a multimode interferometer. Building upon previous work, our scheme consists of a multimode interferometer with single-photon inputs. By using a quantum Fisher information analysis, we show that our scheme gives a constant improvement over other schemes. We also show that our scheme with photon-number-resolving detection approaches the quantum Cram\'er-Rao bound. Moreover, we also consider the probabilistic nature of photon emission at the input, and we study its effect on phase sensitivity. I discuss phase estimation with SU(1,1) interferometer in Chapter 3. We look at phase sensitivity in this interferometer with different input states. Namely, we consider two different phase estimation scheme, one using thermal and squeezed states, and others using coherent and displaced squeezed states with parity and on-off as a detection scheme. We also look into the effect of photon loss inside the interferometer. In Chapter 4, we revisit phase estimation in SU(1,1) interferometer from the perspective of quantum Fisher information. I discuss in detail a longstanding confusion regarding the use of quantum Fisher information in SU(1,1) interferometer. We show that phase averaging or quantum Fisher information matrix method is needed in general for calculating the phase sensitivity which resolves inconsistencies reported in previously published articles.