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:1105.2805 · New Journal of Physics

Parity detection achieves the Heisenberg limit in interferometry with coherent mixed with squeezed vacuum light

Kaushik Parasuram Seshadreesan, Petr M. Anisimov, Hwang Lee, Jonathan P. Dowling

Published Aug 24, 2011• 99 citations
arXivHTMLPDF

Abstract

The interference between coherent and squeezed vacuum light effectively produces path entangled N00N states with very high fidelities. We show that the phase sensitivity of the above interferometric scheme with parity detection saturates the quantum Cramer–Rao bound, which reaches the Heisenberg limit when the coherent and squeezed vacuum light are mixed in roughly equal proportions. For the same interferometric scheme, we draw a detailed comparison between parity detection and a symmetric-logarithmic-derivative-based detection scheme suggested by Ono and Hofmann.

DOI
10.1088/1367-2630/13/8/083026

Related papers

Coherent mixed with squeezed vacuum light interferometry: parity detection hits the Heisenberg limit

Kaushik Parasuram Seshadreesan, Petr M. Anisimov, Hwang Lee +1 more

Mach-Zehnder interferometry based on mixing the coherent and the squeezed vacuum states of light has Heisenberg limited capabilities for phase estimation. This is also, because the quantum Cramer-Rao bound on sensitivity of phase estimation with the above interferometric scheme reaches the Heisenberg limit when the inputs are mixed in hear equal proportions. We show that a detection strategy based on the measurement of parity of photon number in one of the output modes of the interferometer saturates the quantum Cramer-Rao bound of the interferometric scheme, and therefore- as a consequence- hits the Heisenberg limit when the inputs are mixed in equal intensities.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Feb 9, 2012•1 citation

Parity Detection for Heisenberg-limited Metrology with Coherent and Squeezed Vacuum Light

Kaushik Parasuram Seshadreesan, Petr M. Anisimov, Hwang Lee +1 more

The interference between coherent and squeezed vacuum light can produce path entangled states with very high fidelities. We show that Heisenberg-limited phase estimation with the above interferometric scheme can be achieved using parity detection.

Frontiers in Optics•Jan 1, 2011•0 citations

Mach-Zehnder Interferometry at the Heisenberg Limit with Coherent and Squeezed-Vacuum Light

Luca Pezzè, Augusto Smerzi

We show that the phase sensitivity $\ensuremath{\Delta}\ensuremath{\theta}$ of a Mach-Zehnder interferometer illuminated by a coherent state in one input port and a squeezed-vacuum state in the other port is (i) independent of the true value of the phase shift and (ii) can reach the Heisenberg limit $\ensuremath{\Delta}\ensuremath{\theta}\ensuremath{\sim}1/{N}_{T}$, where ${N}_{T}$ is the average number of input particles. We also demonstrate that the Cramer-Rao lower bound of phase sensitivity, $\ensuremath{\Delta}\ensuremath{\theta}\ensuremath{\sim}\phantom{\rule{0ex}{0ex}}1/\sqrt{|\ensuremath{\alpha}{|}^{2}{e}^{2r}+{sinh}^{2}r}$, can be saturated for arbitrary values of the squeezing parameter $r$ and the amplitude of the coherent mode $\ensuremath{\alpha}$ by using a Bayesian phase inference protocol.

arXiv:0705.4631•Physical Review Letters•Feb 19, 2008•359 citations

Quantum Metrology with Two-Mode Squeezed Vacuum: Parity Detection Beats the Heisenberg Limit

Petr M. Anisimov, Gretchen M. Raterman, Aravind Chiruvelli +4 more

We study the sensitivity and resolution of phase measurement in a Mach-Zehnder interferometer with two-mode squeezed vacuum (n photons on average). We show that superresolution and sub-Heisenberg sensitivity is obtained with parity detection. In particular, in our setup, dependence of the signal on the phase evolves n times faster than in traditional schemes, and uncertainty in the phase estimation is better than 1/n, and we saturate the quantum Cramer-Rao bound.

arXiv:0910.5942•Physical Review Letters•Mar 12, 2010•448 citations

Phase sensitivity at the Heisenberg limit in an SU(1,1) interferometer via parity detection

Dong Li, Bryan Gard, Yang Gao +4 more

We theoretically investigate the phase sensitivity with parity detection on an SU(1,1) interferometer with a coherent state combined with a squeezed vacuum state. This interferometer is formed with two parametric amplifiers for beam splitting and recombination instead of beam splitters. We show that the sensitivity of phase estimation approaches the Heisenberg limit and give the corresponding optimal condition. Moreover, we derive the quantum Cram\'er-Rao bound of the SU(1,1) interferometer.

arXiv:1603.09019•Physical Review A•Dec 19, 2016•105 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
The interference between coherent and squeezed vacuum light effectively produces path entangled N00N states with very high fidelities. We show that the phase sensitivity of the above interferometric scheme with parity detection saturates the quantum Cramer–Rao bound, which reaches the Heisenberg limit when the coherent and squeezed vacuum light are mixed in roughly equal proportions. For the same interferometric scheme, we draw a detailed comparison between parity detection and a symmetric-logarithmic-derivative-based detection scheme suggested by Ono and Hofmann.
Mach-Zehnder interferometry based on mixing the coherent and the squeezed vacuum states of light has Heisenberg limited capabilities for phase estimation. This is also, because the quantum Cramer-Rao bound on sensitivity of phase estimation with the above interferometric scheme reaches the Heisenberg limit when the inputs are mixed in hear equal proportions. We show that a detection strategy based on the measurement of parity of photon number in one of the output modes of the interferometer saturates the quantum Cramer-Rao bound of the interferometric scheme, and therefore- as a consequence- hits the Heisenberg limit when the inputs are mixed in equal intensities.
We show that the phase sensitivity $\ensuremath{\Delta}\ensuremath{\theta}$ of a Mach-Zehnder interferometer illuminated by a coherent state in one input port and a squeezed-vacuum state in the other port is (i) independent of the true value of the phase shift and (ii) can reach the Heisenberg limit $\ensuremath{\Delta}\ensuremath{\theta}\ensuremath{\sim}1/{N}_{T}$, where NT{N}_{T}NT​ is the average number of input particles. We also demonstrate that the Cramer-Rao lower bound of phase sensitivity, $\ensuremath{\Delta}\ensuremath{\theta}\ensuremath{\sim}\phantom{\rule{0ex}{0ex}}1/\sqrt{|\ensuremath{\alpha}{|}^{2}{e}^{2r}+{sinh}^{2}r}$, can be saturated for arbitrary values of the squeezing parameter rrr and the amplitude of the coherent mode $\ensuremath{\alpha}$ by using a Bayesian phase inference protocol.
We theoretically investigate the phase sensitivity with parity detection on an SU(1,1) interferometer with a coherent state combined with a squeezed vacuum state. This interferometer is formed with two parametric amplifiers for beam splitting and recombination instead of beam splitters. We show that the sensitivity of phase estimation approaches the Heisenberg limit and give the corresponding optimal condition. Moreover, we derive the quantum Cram\'er-Rao bound of the SU(1,1) interferometer.
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.