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

Physical Review A

Quantum metrology with entangled spin-coherent states of two modes

K. Berrada, S. Abdel‐Khalek, C. H. Raymond Ooi

Published Sep 18, 2012• 111 citations
Publisher

Abstract

Recently, Gerry et al. [Phys. Rev. A 79, 022111 (2009)] studied the violation of the Bell-Clauser-Horne-Shimony-Holt inequality for two-spin systems, prepared in an entanglement of spin-coherent states, the so-called entangled spin-coherent states (ESCSs), and found maximal violations for a large class of states. In this paper, using the Holstein-Primakoff realization (HPR) of angular momentum algebra, we present an improved phase estimation scheme employing ESCSs and demonstrate that increasing the spin number gives the smallest variance in the phase parameter in comparison to NOON states under perfect and lossy conditions. The phase sensitivity of this interferometric scheme with parity detection on one of the output states is discussed.

DOI
10.1103/physreva.86.033823

Related papers

Quantum phase estimation for nonlinear phase shifts with entangled spin coherent states of two modes

K. Berrada, S. Abdel‐Khalek

Recently, we presented (Berrada K, Abdel-Khalek S and Raymond Ooi C H 2012 Phys. Rev. A 86 033823) an improved phase estimation scheme employing entangled spin coherent states (ESCSs) using the Holstein?Primakoff realization of angular momentum algebra. Here, we study the nonlinear phase enhancement from a generalized nonlinearity on ESCSs under perfect and lossy conditions with the same mean photon number and nonlinearity order. The results show that an increase in the spin number gives the smallest variance in the phase parameter in comparison to N00N states for different orders of nonlinearity. Finally, we study the physical properties of the input optical field and explore a connection between this quantity and the output state phase uncertainty. In particular, we show that the Mandel parameter may be used as an indicator of the phase estimation behavior in this interferometric setting.

Laser Physics•Aug 20, 2013•12 citations

Quantum Metrology with Entangled Coherent States

Jaewoo Joo, William J. Munro, Timothy P. Spiller

We present an improved phase estimation scheme employing entangled coherent states and demonstrate that these states give the smallest variance in the phase parameter in comparison to NOON, "bat," and "optimal" states under perfect and lossy conditions. As these advantages emerge for very modest particle numbers, the optical version of entangled coherent state metrology is achievable with current technology.

arXiv:1101.5044•Physical Review Letters•Aug 16, 2011•523 citations

Maximal violations of a Bell inequality by entangled spin-coherent states

Christopher C. Gerry, Adil Benmoussa, Edwin E. Hach +1 more

We study the violation of the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality for two-spin systems, of arbitrary spins ${j}_{1}$ and ${j}_{2}$, prepared in an entanglement of spin-coherent states of each of the spins. We show that the Bell-CHSH inequality is quite robustly violated for a wide range of values of the parameters that specify the spin-coherent states, and, for a particular choice of these parameters, maximal violations are obtained. That is, the violations can reach the Tsirelson bound, $2\sqrt{2}$, for any choices of the spins.

Physical Review A•Feb 12, 2009•16 citations

Quantum metrology with SU(1,1) coherent states in the presence of nonlinear phase shifts

K. Berrada

We present an improved phase estimation scheme employing entangled SU(1,1) coherent states in comparison to NOON and entangled coherent states under perfect and lossy conditions for a fixed mean photon number. The study is also devoted to the phase enhancement of the quantum states resulting from a generalized nonlinearity of the phase shifts, both without and with losses. Furthermore, we show that these states give the smallest variance in the phase parameter for a large number of photons in a different order of nonlinearity. Finally, the phase sensitivity of this interferometric setting with parity detection is discussed.

Physical Review A•Jul 11, 2013•77 citations

Geometric phase in entangled systems: A single-neutron interferometer experiment

Stephan Sponar, Jürgen Klepp, Rudolf Loidl +6 more

The influence of the geometric phase on a Bell measurement, as proposed by Bertlmann et al. [Phys. Rev. A 69, 032112 (2004)] and expressed by the Clauser-Horne-Shimony-Holt (CHSH) inequality, has been observed for a spin-path-entangled neutron state in an interferometric setup. It is experimentally demonstrated that the effect of geometric phase can be balanced by a change in Bell angles. The geometric phase is acquired during a time-dependent interaction with a radiofrequency field. Two schemes, polar and azimuthal adjustment of the Bell angles, are realized and analyzed in detail. The former scheme yields a sinusoidal oscillation of the correlation function $S$, dependent on the geometric phase, such that it varies in the range between $2$ and $2\sqrt{2}$ and therefore always exceeds the boundary value $2$ between quantum mechanic and noncontextual theories. The latter scheme results in a constant, maximal violation of the Bell-like CHSH inequality, where $S$ remains $2\sqrt{2}$ for all settings of the geometric phase.

arXiv:0907.4909•Physical Review A•Apr 30, 2010•25 citations

On the connection between quantum nonlocality and phase sensitivity of two-mode entangled Fock state superpositions

Kaushik Parasuram Seshadreesan, Christoph F. Wildfeuer, Moochan B. Kim +2 more

In two-mode interferometry, for a given total photon number N, entangled Fock state superpositions of the form (Formula presented.) have been considered for phase estimation. Indeed all such states are maximally mode-entangled and violate a Clauser–Horne–Shimony–Holt (CHSH) inequality. However, they differ in their optimal phase estimation capabilities as given by their quantum Fisher informations. The quantum Fisher information is the largest for the N00N state (Formula presented.) and decreases for the other states with decreasing photon number difference between the two modes. We ask the question whether for any particular Clauser–Horne (CH) (or CHSH) inequality, the maximal values of the CH (or the CHSH) functional for the states of the above type follow the same trend as their quantum Fisher informations, while also violating the classical bound whenever the states are capable of sub-shot-noise phase estimation, so that the violation can be used to quantify sub-shot-noise sensitivity. We explore CH and CHSH inequalities in a homodyne setup. Our results show that the amount of violation in those nonlocality tests may not be used to quantify sub-shot-noise sensitivity of the above states.

Civil War Book Review•Mar 1, 2016•1 citation
Recently, Gerry et al. [Phys. Rev. A 79, 022111 (2009)] studied the violation of the Bell-Clauser-Horne-Shimony-Holt inequality for two-spin systems, prepared in an entanglement of spin-coherent states, the so-called entangled spin-coherent states (ESCSs), and found maximal violations for a large class of states. In this paper, using the Holstein-Primakoff realization (HPR) of angular momentum algebra, we present an improved phase estimation scheme employing ESCSs and demonstrate that increasing the spin number gives the smallest variance in the phase parameter in comparison to NOON states under perfect and lossy conditions. The phase sensitivity of this interferometric scheme with parity detection on one of the output states is discussed.
Recently, we presented (Berrada K, Abdel-Khalek S and Raymond Ooi C H 2012 Phys. Rev. A 86 033823) an improved phase estimation scheme employing entangled spin coherent states (ESCSs) using the Holstein?Primakoff realization of angular momentum algebra. Here, we study the nonlinear phase enhancement from a generalized nonlinearity on ESCSs under perfect and lossy conditions with the same mean photon number and nonlinearity order. The results show that an increase in the spin number gives the smallest variance in the phase parameter in comparison to N00N states for different orders of nonlinearity. Finally, we study the physical properties of the input optical field and explore a connection between this quantity and the output state phase uncertainty. In particular, we show that the Mandel parameter may be used as an indicator of the phase estimation behavior in this interferometric setting.
We study the violation of the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality for two-spin systems, of arbitrary spins j1{j}_{1}j1​ and j2{j}_{2}j2​, prepared in an entanglement of spin-coherent states of each of the spins. We show that the Bell-CHSH inequality is quite robustly violated for a wide range of values of the parameters that specify the spin-coherent states, and, for a particular choice of these parameters, maximal violations are obtained. That is, the violations can reach the Tsirelson bound, 222\sqrt{2}22​, for any choices of the spins.
We present an improved phase estimation scheme employing entangled SU(1,1) coherent states in comparison to NOON and entangled coherent states under perfect and lossy conditions for a fixed mean photon number. The study is also devoted to the phase enhancement of the quantum states resulting from a generalized nonlinearity of the phase shifts, both without and with losses. Furthermore, we show that these states give the smallest variance in the phase parameter for a large number of photons in a different order of nonlinearity. Finally, the phase sensitivity of this interferometric setting with parity detection is discussed.
The influence of the geometric phase on a Bell measurement, as proposed by Bertlmann et al. [Phys. Rev. A 69, 032112 (2004)] and expressed by the Clauser-Horne-Shimony-Holt (CHSH) inequality, has been observed for a spin-path-entangled neutron state in an interferometric setup. It is experimentally demonstrated that the effect of geometric phase can be balanced by a change in Bell angles. The geometric phase is acquired during a time-dependent interaction with a radiofrequency field. Two schemes, polar and azimuthal adjustment of the Bell angles, are realized and analyzed in detail. The former scheme yields a sinusoidal oscillation of the correlation function SSS, dependent on the geometric phase, such that it varies in the range between 222 and 222\sqrt{2}22​ and therefore always exceeds the boundary value 222 between quantum mechanic and noncontextual theories. The latter scheme results in a constant, maximal violation of the Bell-like CHSH inequality, where SSS remains 222\sqrt{2}22​ for all settings of the geometric phase.
In two-mode interferometry, for a given total photon number N, entangled Fock state superpositions of the form (Formula presented.) have been considered for phase estimation. Indeed all such states are maximally mode-entangled and violate a Clauser–Horne–Shimony–Holt (CHSH) inequality. However, they differ in their optimal phase estimation capabilities as given by their quantum Fisher informations. The quantum Fisher information is the largest for the N00N state (Formula presented.) and decreases for the other states with decreasing photon number difference between the two modes. We ask the question whether for any particular Clauser–Horne (CH) (or CHSH) inequality, the maximal values of the CH (or the CHSH) functional for the states of the above type follow the same trend as their quantum Fisher informations, while also violating the classical bound whenever the states are capable of sub-shot-noise phase estimation, so that the violation can be used to quantify sub-shot-noise sensitivity. We explore CH and CHSH inequalities in a homodyne setup. Our results show that the amount of violation in those nonlocality tests may not be used to quantify sub-shot-noise sensitivity of the above states.