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We discuss the ultimate precision bounds on the multiparameter estimation of single- and two-mode pure Gaussian states. By leveraging on previous approaches that focused on the estimation of a complex displacement only, we derive the Holevo…

Quantum Physics · Physics 2024-07-24 Gabriele Bressanini , Marco G. Genoni , M. S. Kim , Matteo G. A. Paris

We propose and demonstrate experimentally a projection scheme to measure the quantum phase with a precision beating the standard quantum limit. The initial input state is a twin Fock state $|N,N>$ proposed by Holland and Burnett [Phys. Rev.…

Quantum Physics · Physics 2008-03-27 F. W. Sun , B. H. Liu , Y. X. Gong , Y. F. Huang , Z. Y. Ou , G. C. Guo

Quantum metrology exploits quantum correlations to make precise measurements with limited particle numbers. By utilizing inter- and intra- mode correlations in an optical interferometer, we find a state that combines entanglement and…

Quantum Physics · Physics 2016-04-21 P. A. Knott , T. J. Proctor , A. J. Hayes , J. P. Cooling , J. A. Dunningham

Multimode Gaussian quantum light, including multimode squeezed and/or multipartite quadrature entangled light, is a very general and powerful quantum resource with promising applications to quantum information processing and metrology…

Quantum Physics · Physics 2010-08-05 Olivier Pinel , Julien Fade , Nicolas Treps , Claude Fabre

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

Within the quantum phase representation we derive Heisenberg limits, in closed form, for N00N states and two other classes of states that can perform better in terms of local performance metrics relevant for multiply-peaked distributions.…

Quantum Physics · Physics 2016-03-09 Scott Roger Shepard , Frederick Ira Moxley , Jonathan P. Dowling

Gaussian quantum channels constitute a cornerstone of continuous-variable quantum information science, underpinning a wide array of protocols in quantum optics and quantum metrology. While the action of such channels on arbitrary states is…

Quantum Physics · Physics 2026-02-24 Pritam Chattopadhyay , Saikat Sur , Jonas F. G. Santos

Quantum phase estimation protocols can provide a measuring method of phase shift with precision superior to standard quantum limit (SQL) due to the application of a nonclassical state of light. A squeezed vacuum state, whose variance in one…

Quantum Physics · Physics 2020-04-14 Juan Yu , Yue Qin , Jinliang Qin , Hong Wang , Zhihui Yan , Xiaojun Jia , Kunchi Peng

A two-step optimization is proposed to represent an arbitrary quantum state to a desired accuracy with the least number of gaussians in phase space. The Husimi distribution of the quantum state provides the information to determine the…

Atomic and Molecular Clusters · Physics 2009-11-10 Anatole Kenfack , Jan M Rost , Alfredo M Ozorio de Almeida

We find and investigate the optimal scheme of quantum distributed Gaussian sensing for estimation of the average of independent phase shifts. We show that the ultimate sensitivity is achievable by using an entangled symmetric Gaussian…

Quantum Physics · Physics 2020-04-14 Changhun Oh , Changhyoup Lee , Seok Hyung Lie , Hyunseok Jeong

We propose a machine learning framework for parameter estimation of single mode Gaussian quantum states. Under a Bayesian framework, our approach estimates parameters of suitable prior distributions from measured data. For phase-space…

Quantum Physics · Physics 2021-08-16 Neel Kanth Kundu , Matthew R. McKay , Ranjan K. Mallik

Optimal phase estimation protocols require complex state preparation and readout schemes, generally unavailable or unscalable in many quantum platforms. We develop and analyze a scheme that achieves near-optimal precision up to a constant…

Quantum Physics · Physics 2026-02-16 Su Direkci , Ran Finkelstein , Manuel Endres , Tuvia Gefen

We address the problem of continuous-variable quantum phase estimation in the presence of linear disturbance at the Hamiltonian level, by means of Gaussian probe states. In particular we discuss both unitary and random disturbance, by…

Quantum Physics · Physics 2015-01-26 Douglas Delgado de Souza , Marco G. Genoni , M. S. Kim

We derive several expressions for the quantum Fisher information matrix (QFIM) for the multi-parameter estimation of multi-mode Gaussian quantum states, the corresponding symmetric logarithmic derivatives, and conditions for saturability of…

Quantum Physics · Physics 2019-12-30 Dominik Šafránek

A major obstacle to attain the fundamental precision limit of the phase estimation in an interferometry is the identification and implementation of the optimal measurement. Here we demonstrate that this can be accomplished by the use of…

Quantum Physics · Physics 2017-05-10 Wei Zhong , Yixiao Huang , Xiaoguang Wang , Shi-Liang Zhu

Spin-squeezed states constitute a valuable entanglement resource capable of surpassing the standard quantum limit (SQL). However, spin-squeezed states only enable sub-SQL uncertainty within a narrow parametric window near some specific…

Quantum Physics · Physics 2025-10-10 Jinye Wei , Jungeng Zhou , Yi Shen , Jiahao Huang , Chaohong Lee

We construct a practical method for finding optimal Gaussian probe states for the estimation of parameters encoded by Gaussian unitary channels. This method can be used for finding all optimal probe states, rather than focusing on the…

Quantum Physics · Physics 2016-12-14 Dominik Šafránek , Ivette Fuentes

Quantum correlations can be harnessed to improve the precision in parameter estimation beyond classical capabilities. Under a standard interferometric or rotation protocol, it is well established that the optimal single-mode Gaussian state…

Quantum Physics · Physics 2026-04-14 Rubén Gordillo-Hachuel , Erik Torrontegui , Cristina de Dios , Ricardo Puebla

Squeezed-state interferometry plays an important role in quantum-enhanced optical phase estimation, as it allows the estimation precision to be improved up to the Heisenberg limit by using ideal photon-number-resolving detectors at the…

Quantum Physics · Physics 2017-02-22 P. Liu , P. Wang , W. Yang , G. R. Jin , C. P. Sun

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