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High-precision optical phase stabilization in quantum networks is fundamentally constrained by the strict photon-flux and duty-cycle limits required to avoid disturbing fragile quantum states. This challenge becomes especially critical when…

The measurement problem for the optical phase has been traditionally attacked for noiseless schemes or in the presence of amplitude or detection noise. Here we address estimation of phase in the presence of phase diffusion and evaluate the…

Quantum Physics · Physics 2015-03-17 Marco G. Genoni , Stefano Olivares , Matteo G. A. Paris

Phase sensitivity determines the lowest optical path length (OPL) value that can be detected from the noise floor in a quantitative phase microscopy (QPM) system. The temporal phase sensitivity is known to be limited by both photon…

Quantitative Methods · Quantitative Biology 2024-06-12 Yujie Nie , Renjie Zhou

We investigate the connection between the shot-noise limit in linear interferometers and particle entanglement. In particular, we ask whether or not sub shot-noise sensitivity can be reached with all pure entangled input states of $N$…

Quantum Physics · Physics 2015-05-14 Philipp Hyllus , Otfried Gühne , Augusto Smerzi

Quantum systems in Fock states do not have a phase. When two or more Bose-Einstein condensates are sent into interferometers, they nevertheless acquire a relative phase under the effect of quantum measurements. The usual explanation relies…

Quantum Physics · Physics 2009-05-19 William W. J. Mullin , Franck Laloë

The change of a quantum state can generally only be fully monitored through simultaneous measurements of two non-commuting observables X and Y spanning a phase space. A measurement device that is coupled to the thermal environment provides…

Quantum Physics · Physics 2021-04-20 Jascha Zander , Roman Schnabel

In multimode interferometers, the interaction between several modes brings a high level of complexity to the interpretation of its light patterns. With recent advances, it is possible to selectively excite only a couple of modes inside the…

Optics · Physics 2024-10-22 Yuri Hayashi Isayama

We address the problem of the optimal quantum estimation of the coupling parameter of a bilinear interaction, such as the transmittivity of a beam splitter or the internal phase-shift of an interferometer. The optimal measurement scheme…

Quantum Physics · Physics 2007-05-23 G. Mauro D'Ariano , Matteo G. A. Paris , Paolo Perinotti

The Heisenberg limit is the superior precision available by entanglement sensors. However, entanglementis fragile against dephasing, and there is no known quantum metrology protocol that can achieve Heisenberg limited sensitivity with the…

Quantum Physics · Physics 2018-09-05 Yuichiro Matsuzaki , Shiro Saito , William J. Munro

We study the competition between phase definition and quantum phase fluctuations in interference experiments between independently formed Bose condensates. While phase-sensitive detection of atoms makes the phase progressively better…

Soft Condensed Matter · Physics 2009-10-31 Sigmund Kohler , Fernando Sols

Phase estimation is known to be a robust method for single-qubit gate calibration in quantum computers, while Bayesian estimation is widely used in devising optimal methods for learning in quantum systems. We present Bayesian phase…

Quantum Physics · Physics 2025-05-06 Brennan de Neeve , Andrey V. Lebedev , Vlad Negnevitsky , Jonathan P. Home

Precise measurement of the angular deviation of an object is a common task in science and technology. Many methods use light for this purpose. Some of these exploit interference effects to achieve technological advantages, such as…

Quantum Physics · Physics 2020-08-19 G. H. Aguilar , R. S. Piera , P. L. Saldanha , R. L. de Matos Filho , S. P. Walborn

Distributed quantum sensing leverages quantum correlations among multiple sensors to enhance the precision of parameter estimation beyond classical limits. Most existing approaches target phase estimation and rely on a shared phase…

Quantum Physics · Physics 2026-02-04 Piotr T. Grochowski , Matteo Fadel , Radim Filip

We measured the relative phase of two Bose-Einstein condensates confined in an radio frequency induced double well potential on an atom chip. We observed phase coherence between the separated condensates for times up to 200 ms after…

Other Condensed Matter · Physics 2007-05-23 G. -B. Jo , Y. Shin , S. Will , T. A. Pasquini , M. Saba , W. Ketterle , D. E. Pritchard , M. Vengalattore , M. Prentiss

Entanglement, a key feature of quantum mechanics, is a resource that allows the improvement of precision measurements beyond the conventional bound reachable by classical means. This is known as the standard quantum limit, already defining…

Other Condensed Matter · Physics 2008-12-09 J. Esteve , C. Gross , A. Weller , S. Giovanazzi , M. K. Oberthaler

The use of special quantum states to achieve sensitivities below the limits established by classically behaving states has enjoyed immense success since its inception. In bosonic interferometers, squeezed states, number states and cat…

We give an iterative algorithm for phase estimation of a parameter theta, which is within a logarithmic factor of the Heisenberg limit. Unlike other methods, we do not need any entanglement or an extra rotation gate which can perform…

Quantum Physics · Physics 2010-01-22 Caleb J O'Loan

Quantum metrology is the state-of-the-art measurement technology. It uses quantum resources to enhance the sensitivity of phase estimation beyond what reachable within classical physics. While single parameter estimation theory has been…

Compact interferometers, called phasemeters, make it possible to operate over a large range while ensuring a high resolution. Such performance is required for the stabilization of large instruments dedicated to experimental physics such as…

Instrumentation and Methods for Astrophysics · Physics 2018-12-03 Jennifer Watchi , Sam Cooper , Binlei Ding , Conor M. Mow-Lowry , Christophe Collette

We investigate the ultimate precision limits for quantum phase estimation in terms of the coherence, $C$, of the probe. For pure states, we give the minimum estimation variance attainable, $V(C)$, and the optimal state, in the asymptotic…

Quantum Physics · Physics 2022-07-13 D. Munoz-Lahoz , J. Calsamiglia , J. A. Bergou , E. Bagan