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We calculate the quantum Cram\'er--Rao bound for the sensitivity with which one or several parameters, encoded in a general single-mode Gaussian state, can be estimated. This includes in particular the interesting case of mixed Gaussian…

Quantum Physics · Physics 2015-06-16 O. Pinel , P. Jian , N. Treps , C. Fabre , and D. Braun

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 show that the quantum Cram\'er-Rao bound on the precision of measurements of the optical phase gradient, or the wavefront tilt, with a beam of finite width is consistent with the Heisenberg uncertainty principle for a single-photon…

Quantum Physics · Physics 2020-07-22 Walker Larson , Bahaa E. A. Saleh

We obtain the ultimate quantum limit for estimating the transverse separation of two thermal point sources using a given imaging system with limited spatial bandwidth. We show via the quantum Cram\'er-Rao bound that, contrary to the…

Quantum Physics · Physics 2016-11-29 Ranjith Nair , Mankei Tsang

The method of maximum likelihood estimation (MLE) is a widely used statistical approach for estimating the values of one or more unknown parameters of a probabilistic model based on observed data. In this tutorial, I briefly review the…

Data Analysis, Statistics and Probability · Physics 2018-12-03 Anthony Vella

The quantum statistical fluctuations of the electromagnetic field establish a limit, known as the shot-noise limit, on the sensitivity of optical measurements performed with classical technologies. However, quantum technologies are not…

Here, we present a proof-of-principle high-dimensional quantum key distribution (QKD) protocol utilizing the position and momentum entanglement of photon pairs. The protocol exploits the fact that position and momentum form mutually…

Quantum Physics · Physics 2026-03-09 Lukas Scarfe , Yingwen Zhang , Ebrahim Karimi

We study the sensitivity and resolution of phase measurement in a Mach-Zehnder interferometer with two-mode squeezed vacuum (<n> photons on average). We show that super-resolution and sub-Heisenberg sensitivity is obtained with parity…

Among the known resources of quantum metrology, one of the most practical and efficient is squeezing. Squeezed states of atoms and light improve the sensing of the phase, magnetic field, polarization, mechanical displacement. They promise…

Quantum Physics · Physics 2021-05-18 Gaetano Frascella , Sascha Agne , Farid Ya. Khalili , Maria V. Chekhova

The canonical Mach-Zehnder interferometer fed with a coherent state and a squeezed-vacuum state of equal intensities is theoretically predicted to achieve Heisenberg scaling in phase sensitivity. However, this ultimate performance is…

Quantum Physics · Physics 2026-05-04 Yi Gu , Song-Ping Wang , Wei Zhong

We study a new image sensor that is reminiscent of traditional photographic film. Each pixel in the sensor has a binary response, giving only a one-bit quantized measurement of the local light intensity. To analyze its performance, we…

Information Theory · Computer Science 2015-05-28 Feng Yang , Yue M. Lu , Luciano Sbaiz , Martin Vetterli

Quantum metrology protocols are typically designed around the assumption that we have an abundance of measurement data, but recent practical applications are increasingly driving interest in cases with very limited data. In this regime the…

Quantum Physics · Physics 2019-04-18 Jesús Rubio , Jacob Dunningham

The simultaneous two-parameter estimation problem in single squeezed-light Mach-Zehnder interferometer with double-port homodyne detection is investigated in this work. The analytical form of the two-parameter quantum Cramer-Bao bound…

Quantum Physics · Physics 2024-02-19 Li-li Hou , Jian-Dong Zhang , Kai-Min Zheng , Shuai Wang

Quantum parameter estimation is central to many fields such as quantum computation, communications and metrology. Optimal estimation theory has been instrumental in achieving the best accuracy in quantum parameter estimation, which is…

Quantum Physics · Physics 2015-06-18 Shibdas Roy , Ian R. Petersen , Elanor H. Huntington

We explore the advantages offered by twin light beams produced in parametric down-conversion for precision measurement. The symmetry of these bipartite quantum states, even under losses, suggests that monitoring correlations between the…

Quantum Physics · Physics 2010-07-20 Hugo Cable , Gabriel A. Durkin

Squeezed-light generation in photonic integrated circuits (PICs) is essential for scalable continuous-variable (CV) quantum information processing. By suppressing quantum fluctuations below the shot-noise limit, squeezed states enable…

Quantum Physics · Physics 2025-09-15 Shuai Liu , Kailu Zhou , Yuheng Zhang , Abdulkarim Hariri , Nicholas Reynolds , Bo-Han Wu , Zheshen Zhang

We investigate the prospects of using two-mode intensity squeezed twin-beams, generated in Rb vapor, to improve the sensitivity of spectroscopic measurements by engaging two-photon Raman transitions. As a proof of principle demonstration,…

Atomic Physics · Physics 2021-04-21 Nikunjkumar Prajapati , Ziqi Niu , Irina Novikova

Quantum metrology derives its capabilities from the careful employ of quantum resources for carrying out measurements. This advantage, however, relies on refined data postprocessing, assessed based on the variance of the estimated…

Quantum optical metrology aims to identify ultimate sensitivity bounds for the estimation of parameters encoded into quantum states of the electromagnetic field. In many practical applications, including imaging, microscopy, and remote…

Quantum Physics · Physics 2023-02-15 Giacomo Sorelli , Manuel Gessner , Nicolas Treps , Mattia Walschaers

Squeezing a quantum state along a specific direction has long been recognized as a crucial technique for enhancing the precision of quantum metrology by reducing parameter uncertainty. However, practical quantum metrology often involves the…