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

arXiv:1207.0494 · Physical Review A

Phase estimation at the quantum Cramér-Rao bound via parity detection

Kaushik Parasuram Seshadreesan, Sejong Kim, Jonathan P. Dowling, Hwang Lee

Published Apr 25, 2013• 93 citations
arXivHTMLPDF

Abstract

We show that, in two-path optical interferometry, the measurement of photon number parity achieves maximal phase sensitivity at the quantum Cram\'er-Rao bound for a certain type of path-symmetric states. All pure states of light proposed for sub--shot-noise phase sensitivity thus far in the literature are of the form of these path-symmetric states. Thus, parity measurement presents an optimal detection strategy for all of them. Our scheme is applicable for local phase estimation.

DOI
10.1103/physreva.87.043833

Related papers

All path-symmetric pure states achieve their maximal phase sensitivity in conventional two-path interferometry

Holger Friedrich Hofmann

It is shown that the condition for achieving the quantum Cramer-Rao bound of phase estimation in conventional two-path interferometers is that the state is symmetric with regard to an (unphysical) exchange of the two paths. Since path symmetry is conserved under phase shifts, the maximal phase sensitivity can be achieved at arbitrary bias phases, indicating that path-symmetric states can achieve their quantum Cramer-Rao bound in Bayesian estimates of a completely unknown phase.

arXiv:0812.0044•Physical Review A•Mar 16, 2009•124 citations

Path-Symmetric States and Parity Detection in Quantum Optical Interferometry

Kaushik Parasuram Seshadreesan, Sejong Kim, Bhaskar Roy Bardhan +2 more

In optical phase estimation, pure states that achieve maximal phase sensitivities with number counting, are symmetric with respect to a certain exchange of paths. We prove the optimality of photon-number parity detection for such path-symmetric states.

The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting•Jan 1, 2013•0 citations

Super-sensitive phase estimation with coherent boosted light using parity measurements

Lan Xu, Qing-Shou Tan

We consider a passive and active hybrid interferometer for phase estimation, which can reach the sub-shot-noise limit in phase sensitivity with only the cheapest coherent sources. This scheme is formed by adding an optical parametric amplifier before a Mach–Zehnder interferometer. It is shown that our hybrid protocol can obtain a better quantum Cramer–Rao bound than the pure active (e.g., SU(1,1)) interferometer, and this precision can be reached by implementing the parity measurements. Furthermore, we also draw a detailed comparison between our scheme and the scheme suggested by Caves [ Phys. Rev. D 23 1693 (1981)], and it is found that the optimal phase sensitivity gain obtained in our scheme is always larger than that in Caves’ scheme.

Chinese Physics B•Jan 1, 2018•1 citation

Quantum phase estimation using path-symmetric entangled states

Su‐Yong Lee, Chang-Woo Lee, Jaehak Lee +1 more

We study the sensitivity of phase estimation using a generic class of path-symmetric entangled states |φ〉|0〉 + |0〉|φ〉, where an arbitrary state |φ〉 occupies one of two modes in quantum superposition. With this generalization, we identify the fundamental limit of phase estimation under energy constraint that is characterized by the photon statistics of the component state |φ〉. We show that quantum Cramer-Rao bound (QCRB) can be indefinitely lowered with super-Poissonianity of the state |φ〉. For possible measurement schemes, we demonstrate that a full photon-counting employing the path-symmetric entangled states achieves the QCRB over the entire range [0, 2π] of unknown phase shift ϕ whereas a parity measurement does so in a certain confined range of ϕ. By introducing a component state of the form , we particularly show that an arbitrarily small QCRB can be achieved even with a finite energy in an ideal situation. This component state also provides the most robust resource against photon loss among considered entangled states over the range of the average input energy Nav > 1. Finally we propose experimental schemes to generate these path-symmetric entangled states for phase estimation.

arXiv:1505.06000•Scientific Reports•Jul 26, 2016•36 citations

Quantum optical interferometry via general photon-subtracted two-mode squeezed states*

Li-Li Hou, Jianzhong Xue, Yongxing Sui +1 more

We investigate the sensitivity of phase estimation in a Mach–Zehnder interferometer with photon-subtracted two-mode squeezed vacuum states. Our results show that, for given initial squeezing parameter, both symmetric and asymmetric photon subtractions can further improve the quantum Cramér–Rao bound (i.e., the ultimate phase sensitivity), especially for single-mode photon subtraction. On the other hand, the quantum Cramér–Rao bound can be reached by parity detection for symmetric photon-subtracted two-mode squeezed vacuum states at particular values of the phase shift, but it is not valid for asymmetric photon-subtracted two-mode squeezed vacuum states. In addition, compared with the two-mode squeezed vacuum state, the phase sensitivity via parity detection with asymmetric photon-subtracted two-mode squeezed vacuum states will be getting worse. Thus, parity detection may not always be the optimal detection scheme for nonclassical states of light when they are considered as the interferometer states.

Chinese Physics B•Aug 6, 2019•7 citations

Quantum Cramer-Rao bound and parity measurement

Aravind Chiruvelli, Hwang Lee

We show, by using parity detection, that the phase estimate obtained from the linear error propagation formula, indeed saturates the lower bound set by maximizing quantum Fisher information for several of the well-known states, proposed for the Heisenberg limited interferometry. Our results show that one can achieve the quantum Cram´er-Rao bound, by simply counting the number of photons which is not very far from actual realization.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Feb 8, 2010•2 citations
We show that, in two-path optical interferometry, the measurement of photon number parity achieves maximal phase sensitivity at the quantum Cram'er-Rao bound for a certain type of path-symmetric states. All pure states of light proposed for sub--shot-noise phase sensitivity thus far in the literature are of the form of these path-symmetric states. Thus, parity measurement presents an optimal detection strategy for all of them. Our scheme is applicable for local phase estimation.
We consider a passive and active hybrid interferometer for phase estimation, which can reach the sub-shot-noise limit in phase sensitivity with only the cheapest coherent sources. This scheme is formed by adding an optical parametric amplifier before a Mach–Zehnder interferometer. It is shown that our hybrid protocol can obtain a better quantum Cramer–Rao bound than the pure active (e.g., SU(1,1)) interferometer, and this precision can be reached by implementing the parity measurements. Furthermore, we also draw a detailed comparison between our scheme and the scheme suggested by Caves [ Phys. Rev. D 23 1693 (1981)], and it is found that the optimal phase sensitivity gain obtained in our scheme is always larger than that in Caves’ scheme.
We study the sensitivity of phase estimation using a generic class of path-symmetric entangled states |φ〉|0〉 + |0〉|φ〉, where an arbitrary state |φ〉 occupies one of two modes in quantum superposition. With this generalization, we identify the fundamental limit of phase estimation under energy constraint that is characterized by the photon statistics of the component state |φ〉. We show that quantum Cramer-Rao bound (QCRB) can be indefinitely lowered with super-Poissonianity of the state |φ〉. For possible measurement schemes, we demonstrate that a full photon-counting employing the path-symmetric entangled states achieves the QCRB over the entire range [0, 2π] of unknown phase shift ϕ whereas a parity measurement does so in a certain confined range of ϕ. By introducing a component state of the form , we particularly show that an arbitrarily small QCRB can be achieved even with a finite energy in an ideal situation. This component state also provides the most robust resource against photon loss among considered entangled states over the range of the average input energy Nav > 1. Finally we propose experimental schemes to generate these path-symmetric entangled states for phase estimation.
We investigate the sensitivity of phase estimation in a Mach–Zehnder interferometer with photon-subtracted two-mode squeezed vacuum states. Our results show that, for given initial squeezing parameter, both symmetric and asymmetric photon subtractions can further improve the quantum Cramér–Rao bound (i.e., the ultimate phase sensitivity), especially for single-mode photon subtraction. On the other hand, the quantum Cramér–Rao bound can be reached by parity detection for symmetric photon-subtracted two-mode squeezed vacuum states at particular values of the phase shift, but it is not valid for asymmetric photon-subtracted two-mode squeezed vacuum states. In addition, compared with the two-mode squeezed vacuum state, the phase sensitivity via parity detection with asymmetric photon-subtracted two-mode squeezed vacuum states will be getting worse. Thus, parity detection may not always be the optimal detection scheme for nonclassical states of light when they are considered as the interferometer states.