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Quantum-limited estimation of an optical phase using adaptive (i.e. real-time feedback) techniques is reviewed. One case is explored in detail, as it can be understood using only elementary concepts such as photonic shot-noise and error…

Quantum Physics · Physics 2007-05-23 H. M. Wiseman

Phase-insensitive optical amplifiers uniformly amplify each quadrature of an input field and are of both fundamental and technological importance. We find the quantum limit on the precision of estimating the gain of a quantum-limited…

Quantum Physics · Physics 2022-05-09 Ranjith Nair , Guo Yao Tham , Mile Gu

We consider the phase sensing via weak optical coherent state at quantum limit precision. A new detection scheme for the phase estimation is proposed which is inspired by the suboptimal quantum measurement in coherent optical communication.…

Quantum Physics · Physics 2016-09-28 Shuro Izumi , Masahiro Takeoka , Kentaro Wakui , Mikio Fujiwara , Kazuhiro Ema , Masahide Sasaki

The Gaussian state description of continuous variables is adapted to describe the quantum interaction between macroscopic atomic samples and continuous-wave light beams. The formalism is very efficient: a non-linear differential equation…

Quantum Physics · Physics 2007-05-23 L. B. Madsen , K. Mølmer

Constant-envelope signals are widely used in mobile edge applications and wireless communication systems for their hardware-friendly design, energy efficiency, and reliability. However, reliable detection with simple, power-efficient…

Signal Processing · Electrical Eng. & Systems 2025-11-25 Mu Jia , Junting Chen , Ying-Chang Liang , Pooi-Yuen Kam

We consider the problem of determining the spatial phase profile of a single-mode electromagnetic field. Our attention is on input states that are a statistical mixture of displaced and squeezed number states, a superset of Gaussian states.…

Optics · Physics 2024-07-09 Jacob Trzaska , Amit Ashok

Continuous-time measurements are instrumental for a multitude of tasks in quantum engineering and quantum control, including the estimation of dynamical parameters of open quantum systems monitored through the environment. However, such…

Quantum Physics · Physics 2023-04-12 Alfred Godley , Madalin Guta

We derive a phase-entanglement criterion for two bosonic modes which is immune to number fluc- tuations, using the generalized Moore-Penrose inverse to normalize the phase-quadrature operator. We also obtain a phase-squeezing criterion that…

Quantum Physics · Physics 2014-05-09 Q. Y. He , T. G. Vaughan , P. D. Drummond , M. D. Reid

We consider the decoherence of a pseudo-spin ensemble under collective random rotations, and study, both theoretically and experimentally, how a nondestructive measurement combined with real-time feedback correction can protect the state…

We present a measurement scheme capable of achieving the quantum limit of parameter estimation using an adaptive strategy that minimizes the parameter's variance at each step. The adaptive rule we propose makes the scheme robust against…

Quantum Physics · Physics 2012-03-09 Paola Cappellaro

Estimation of the properties of a physical system with minimal uncertainty is a central task in quantum metrology. Optical phase estimation is at the center of many metrological tasks where the value of a physical parameter is mapped to the…

Quantum Physics · Physics 2020-09-29 M. T. DiMario , F. E. Becerra

Quantum sensor networks (QSNs) have been widely studied for their potential of precise measurements. While most QSN research has focused on estimating continuous variables, recent studies have explored discrete-variable estimation. Here, we…

Scheme for optimal spin state estimation is considered in analogy with phase detection in interferometry. Recently reported coherent measurements yielding the average fidelity (N+1)/(N+2) for N particle system corresponds to the standard…

Quantum Physics · Physics 2009-10-31 Z. Hradil , M. Dusek

Using continuous wave superposition of spatial modes, we demonstrate experimentally displacement measurement of a light beam below the standard quantum limit. Multimode squeezed light is obtained by mixing a vacuum squeezed beam and a…

Quantum Physics · Physics 2009-11-07 N. Treps , U. Andersen , B. Buchler , P. K. Lam , A. Maitre , H. -A. Bachor , C. Fabre

Time-bin encoded photon pairs enable robust, decoherence-resistant transmission through optical fibers for long-distance quantum communication, where phase noise poses a critical limitation to stable operation. Here, we implement an…

Quantum Physics · Physics 2025-10-28 P. M. Berto , F. CampodÓnico , A. A. Matoso , S. Vergara , P. A. Coelho , G. Lima , S. PÁdua , J. CariÑe

Realizing a sensitive photon-number-dependent phase shift on a light beam is required both in classical and quantum photonics. It may lead to new applications for classical and quantum photonics machine learning or pave the way for…

We derive the form of the quantum filter equation describing the continuous observation of the phase of a quantum system in an arm of an interferometer via non-demolition measurements when the statistics of an input field used for the…

Quantum Physics · Physics 2016-01-19 John Gough

We theoretically study the quantum receivers with adaptive measurements feedback for discriminating quadrature amplitude modulation (QAM) coherent states in terms of average symbol error rate. For rectangular 16-QAM signal set, with…

Quantum Physics · Physics 2015-04-14 Tian Chen , Ke Li , Yuan Zuo , Bing Zhu

Quantum phase estimation is one of the most important tools in quantum algorithms. It can be made non-adaptive (meaning all applications of the unitary $U_\phi$ happen simultaneously) without using more applications of $U_\phi$, albeit at…

Quantum Physics · Physics 2025-11-10 Noah Linden , Ronald de Wolf

Millimeter-wave communication has the potential to deliver orders of magnitude increases in mobile data rates. A key design challenge is to enable rapid beam alignment with phased arrays. Traditional millimeter-wave systems require a high…

Signal Processing · Electrical Eng. & Systems 2020-10-06 Han Yan , Benjamin W. Domae , Danijela Cabric