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This paper, following [M. Ozawa, Phys. Rev. Lett. 60, 385 (1988)], reports a refutation of the claim that for monitoring the position of a free mass such as gravitational-wave interferometers the sensitivity is limited by the so called…

Quantum Physics · Physics 2018-09-05 Masanao Ozawa

The measurement result of the moved distance for a free mass m during the time t between two position measurements cannot be predicted with uncertainty smaller than sqrt{hbar t/2m}. This is formulated as a standard quantum limit (SQL) and…

Quantum Physics · Physics 2013-05-29 Seiji Kosugi

I utilize the Caves-Milburn model for continuous position measurements to formulate a broadband version of the Standard Quantum Limit (SQL) for monitoring the position of a free mass, and illustrate the use of Kalman filtering to recover…

Quantum Physics · Physics 2012-01-20 Hideo Mabuchi

Quantum metrology aims to enhance measurement precision beyond the standard quantum limit (SQL), the benchmark set by classical resources, enabling advances in sensing, imaging, and fundamental physics. A critical milestone beyond the SQL…

Quantum Physics · Physics 2025-08-19 Kimin Park , Tanjung Krisnanda , Yvonne Gao , Radim Filip

Quantum mechanics dictates that the precision of physical measurements must be subject to certain constraints. In the case of inteferometric displacement measurements, these restrictions impose a 'standard quantum limit' (SQL), which…

Quantum Physics · Physics 2019-08-13 David Mason , Junxin Chen , Massimiliano Rossi , Yeghishe Tsaturyan , Albert Schliesser

Quantum-enhanced measurements use quantum mechanical effects in order to enhance the sensitivity of the measurement of classical quantities, such as the length of an optical cavity. The major goal is to beat the standard quantum limit…

Quantum Physics · Physics 2011-03-10 Daniel Braun , John Martin

In this paper, we show how the Robertson uncertainty relation gives certain intrinsic quantum limits of measurements in the most general and rigorous mathematical treatment. A general lower bound for the product of the root-mean-square…

Quantum Physics · Physics 2015-05-20 Masanao Ozawa

Precision measurement plays a crucial role in all fields of science. The use of entangled sensors in quantum metrology improves the precision limit from the standard quantum limit (SQL) to the Heisenberg limit (HL). To date, most…

The standard quantum limit (SQL), also known as the shot-noise limit, defines how quantum fluctuations of light constrain measurement precision. In a benchmark experiment using the Mach-Zehnder interferometer (MZI), where a coherent state…

The typical bound on parameter estimation, known as the standard quantum limit (SQL), can be surpassed by exploiting quantum resources such as entanglement. To estimate the magnetic probe field, we propose a quantum sensor based on a…

Quantum Physics · Physics 2025-07-01 Monika Mothsara , Leela Ganesh Chandra Lakkaraju , Srijon Ghosh , Aditi Sen De

State-of-the-art sensors of force, motion and magnetic fields have reached the sensitivity where the quantum noise of the meter is significant or even dominant. In particular, the sensitivity of the best optomechanical devices has reached…

Quantum Physics · Physics 2021-05-05 Farid Ya. Khalili , Emil Zeuthen

Quantum mechanics places noise limits and sensitivity restrictions on physical measurements. The balance between unwanted backaction and the precision of optical measurements impose a standard quantum limit (SQL) on interferometric systems.…

Quantum noise is an important issue for advanced LIGO. Although it is in principle possible to beat the Standard Quantum Limit (SQL), no practical recipe has been found yet. This paper dicusses quantum noise in the context of speedmeter-a…

General Relativity and Quantum Cosmology · Physics 2009-10-28 F. Ya. Khalili , Yu. Levin

Quantum entanglement and quantum squeezing are two most typical approaches to beat the standard quantum limit (SQL) of the sensitive phase estimations in quantum metrology. Each of them has already been utilized individually to improve the…

Quantum Physics · Physics 2023-08-28 X. N. Feng , M. Zhang , L. F. Wei

Quantum-enhanced measurements use highly non-classical quantum states in order to enhance the precision of the measurement of classical quantities, like the length of an optical cavity. The major goal is to beat the standard quantum limit…

Quantum Physics · Physics 2009-05-29 Daniel Braun , John Martin

Precision metrology underpins scientific and technological advancements. Quantum metrology offers a pathway to surpass classical sensing limits by leveraging quantum states and measurement strategies. However, measuring multiple…

Quantum probes using $N$ uncorrelated particles give a limit on the measurement sensitivity referred to as the standard quantum limit (SQL). The SQL, however, can be overcome by exploiting quantum entangled states, such as spin squeezed…

In this review, we study how a hybrid optomechanical system (OMS), in which a quantum micro- or nano-mechanical oscillator (MO) is coupled to the electromagnetic (EM) radiation pressure, consisting of an ensemble of ultracold atoms or an…

Quantum Physics · Physics 2021-04-20 Ali Motazedifard , A. Dalafi , M. H. Naderi

We report a quantum measurement beyond the standard quantum limit (SQL) for the amplitude of a small displacement acting on a cavity field. This measurement uses as resource an entangled mesoscopic state, prepared by the resonant…

Non-vanishing fluctuations of the vacuum state are a salient feature of quantum theory. These fluctuations fundamentally limit the precision of quantum sensors. Nowadays, several systems such as optical clocks, gravitational wave detectors,…

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