Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Nonlinear Optics

Quantum metrology in the joint measurement of multiple non-commuting observables with SU(1,1) interferometer

Xiaoying Li, Yuhong Liu, Jiamin Li, Liang Cui, Nan Huo, Z. Y. Ou

Published Jan 1, 2017• 0 citations
Publisher

Abstract

We simultaneously measure the multiple non-commuting observables carried by an optical field with the SU(1,1) nonlinear interferometer, and demonstrate that joint measurement of three non-commuting observables have a sensitivity beating the standard quantum limit.
DOI
10.1364/nlo.2017.nw3b.2

Related papers

Quantum Enhanced Joint Multi-Parameter Measurement

Jiamin Li, Yuhong Liu, Liang Cui +3 more

We study simultaneously measure the multiple non-commuting observables by using the SU(1,1) nonlinear interferometer, and show that joint measurement of each non-commuting observables can achieve a sensitivity beating the standard quantum limit.

Conference on Lasers and Electro-Optics•Jan 1, 2018•0 citations

Quantum Metrology in the Joint Measurement of Multiple Parameters Encoded in Non-Commuting Observables with SU(1,1) Interferometer

Yuhong Liu, Jiamin Li, Xiaoying Li +2 more

Joint measurement of phase and amplitude modulations on a probe field is performed with an SU(1,1) interferometer. Signal-to-noise ratios in the joint measurement simultaneously beat the classical limit by 1dB.

Frontiers in Optics•Jan 1, 2017•0 citations

Quantum enhanced joint measurement of multiple non-commuting observables with SU(1,1) interferometer

Yuhong Liu, Jiamin Li, Liang Cui +4 more

Heisenberg uncertainty relation in quantum mechanics sets the limit on the measurement precision of non-commuting observables, which prevents us from measuring them accurately at the same time. In some applications, however, the information are embedded in two or more non-commuting observables. On the other hand, quantum entanglement allows us to infer through Einstein-Podolsky-Rosen correlations two conjugate observables with precision better than what is allowed by Heisenberg uncertainty relation. With the help of the newly developed SU(1,1) interferometer, we implement a scheme to measure jointly information encoded in multiple non-commuting observables of an optical field with a signal-to-noise ratio improvement of about 20 % over the standard quantum limit on all measured quantities simultaneously. This scheme can be generalized to the joint measurement of information in arbitrary number of non-commuting observables.

arXiv:1712.01553•Dec 5, 2017•46 citations

Joint measurement of multiple noncommuting parameters

Jiamin Li, Yuhong Liu, Liang Cui +4 more

Although quantum metrology allows us to make precision measurements beyond the standard quantum limit, it mostly works on the measurement of only one observable due to the Heisenberg uncertainty relation on the measurement precision of noncommuting observables for one system. In this paper, we study the schemes of joint measurement of multiple observables which do not commute with each other using the quantum entanglement between two systems. We focus on analyzing the performance of a SU(1,1) nonlinear interferometer on fulfilling the task of joint measurement. The results show that the information encoded in multiple noncommuting observables on an optical field can be simultaneously measured with a signal-to-noise ratio higher than the standard quantum limit, and the ultimate limit of each observable is still the Heisenberg limit. Moreover, we find a resource conservation rule for the joint measurement.

arXiv:1711.10857•Physical Review A•May 29, 2018•26 citations

Quantum enhanced joint measurement of two conjugate observables with an SU(1, 1) interferometer

Yuhong Liu, Jiamin Li, Nan Huo +2 more

We jointly measure the phase and amplitude modulation of an optical field with the newly developed SU(1,1) interferometer. We simultaneously achieve a signal-to-noise ratio improvement of 1.1 and 1 dB over the standard quantum limit in amplitude and phase measurement.

Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR)•Jul 1, 2017•0 citations

Quantum metrology for simultaneously estimating the linear and nonlinear phase shifts

Jing Cheng

Quantum metrology allows the enhanced precision on estimating phase shifts in an optical interferometer to reach the $\ensuremath{\propto}1/N$ scaling of precision ($N$ is the mean photon number of the light field). But when $N$ is very large, the nonlinear optical effects may be nonnegligible. Here we investigate theoretically the quantum uncertainty bounds for simultaneously detecting the linear and nonlinear phase shifts. Focusing our attentions only on the linear and the nonlinear Kerr phase shifts, we find the NOON states can not be used to measure the two phase parameters. Using the entangled coherent states, the estimation precision is limited by the $1/{N}^{1/2}$ ($1/{N}^{3/2}$) scaling for the linear (nonlinear) phase. To increase the precisions and beat the standard quantum limit, we show that the entangled Schr\"odinger-cat states can be used to reach the $1/N$ scaling for the linear phase and $1/{N}^{2}$ scaling for the nonlinear phase.

Physical Review A•Dec 29, 2014•24 citations
Heisenberg uncertainty relation in quantum mechanics sets the limit on the measurement precision of non-commuting observables, which prevents us from measuring them accurately at the same time. In some applications, however, the information are embedded in two or more non-commuting observables. On the other hand, quantum entanglement allows us to infer through Einstein-Podolsky-Rosen correlations two conjugate observables with precision better than what is allowed by Heisenberg uncertainty relation. With the help of the newly developed SU(1,1) interferometer, we implement a scheme to measure jointly information encoded in multiple non-commuting observables of an optical field with a signal-to-noise ratio improvement of about 20 % over the standard quantum limit on all measured quantities simultaneously. This scheme can be generalized to the joint measurement of information in arbitrary number of non-commuting observables.
Although quantum metrology allows us to make precision measurements beyond the standard quantum limit, it mostly works on the measurement of only one observable due to the Heisenberg uncertainty relation on the measurement precision of noncommuting observables for one system. In this paper, we study the schemes of joint measurement of multiple observables which do not commute with each other using the quantum entanglement between two systems. We focus on analyzing the performance of a SU(1,1) nonlinear interferometer on fulfilling the task of joint measurement. The results show that the information encoded in multiple noncommuting observables on an optical field can be simultaneously measured with a signal-to-noise ratio higher than the standard quantum limit, and the ultimate limit of each observable is still the Heisenberg limit. Moreover, we find a resource conservation rule for the joint measurement.
Quantum metrology allows the enhanced precision on estimating phase shifts in an optical interferometer to reach the $\ensuremath{\propto}1/N$ scaling of precision (NNN is the mean photon number of the light field). But when NNN is very large, the nonlinear optical effects may be nonnegligible. Here we investigate theoretically the quantum uncertainty bounds for simultaneously detecting the linear and nonlinear phase shifts. Focusing our attentions only on the linear and the nonlinear Kerr phase shifts, we find the NOON states can not be used to measure the two phase parameters. Using the entangled coherent states, the estimation precision is limited by the 1/N1/21/{N}^{1/2}1/N1/2 (1/N3/21/{N}^{3/2}1/N3/2) scaling for the linear (nonlinear) phase. To increase the precisions and beat the standard quantum limit, we show that the entangled Schr\"odinger-cat states can be used to reach the 1/N1/N1/N scaling for the linear phase and 1/N21/{N}^{2}1/N2 scaling for the nonlinear phase.