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:2311.17845 · Physical Review A

Error estimation of different schemes to measure spin-squeezing inequalities

Jan Lennart Bönsel, Satoya Imai, Ye‐Chao Liu, Otfried Gühne

Published Aug 7, 2024• 1 citation
arXivHTMLPDF

Abstract

How can we analyze quantum correlations in large and noisy systems without quantum state tomography? An established method is to measure total angular momenta and employ the so-called spin-squeezing inequalities based on their expectations and variances. This allows detection of metrologically useful entanglement, but efficient strategies for estimating such nonlinear quantities have yet to be determined. In this paper we show that spin-squeezing inequalities can not only be evaluated by measurements of the total angular momentum but also by two-qubit correlations, either involving all pair correlations or randomly chosen pair correlations. Then we analyze the estimation errors of our approaches in terms of a hypothesis test. For this purpose, we discuss how error bounds can be derived for nonlinear estimators with the help of their variances, characterizing the probability of falsely detecting a separable state as entangled. We focus on the spin-squeezing inequalities in multiqubit systems. Our methods, however, can also be applied to spin-squeezing inequalities for qudits or for the statistical treatment of other nonlinear parameters of quantum states.

DOI
10.1103/physreva.110.022410

Related papers

Spin squeezing and entanglement

Géza Tóth, Christian Knapp, Otfried Gühne +1 more

What is the relation between spin squeezing and entanglement? To clarify this, we derive the full set of generalized-spin-squeezing inequalities for the detection of entanglement. These are inequalities for the mean values and variances of the collective angular-momentum components ${J}_{k}$. They can be used for the experimental detection of entanglement in a system of spin-$\frac{1}{2}$ particles in which the spins cannot be individually addressed. We present various sets of inequalities that can detect all entangled states that can be detected based on the knowledge of (i) the mean values and variances of ${J}_{k}$ in three orthogonal directions, or (ii) the variances of ${J}_{k}$ in three orthogonal directions, or (iii) the mean values of ${J}_{k}^{2}$ in three orthogonal directions, or (iv) the mean values and variances of ${J}_{k}$ in arbitrary directions. We compare our inequalities to known spin-squeezing entanglement criteria and discuss to which extent spin squeezing is related to entanglement in the reduced two-qubit states. Finally, we apply our criteria for the detection of entanglement in spin models, showing that they can be used to detect bound entanglement in these systems.

arXiv:0806.1048•Physical Review A•Apr 27, 2009•222 citations

Spin squeezing and entanglement for an arbitrary spin

Giuseppe Vitagliano, Iagoba Apellaniz, I. L. Egusquiza +1 more

A complete set of generalized spin-squeezing inequalities is derived for an ensemble of particles with an arbitrary spin. Our conditions are formulated with the first and second moments of the collective angular momentum coordinates. A method for mapping the spin-squeezing inequalities for spin-$\frac{1}{2}$ particles to entanglement conditions for spin-$j$ particles is also presented. We apply our mapping to obtain a generalization of the original spin-squeezing inequality to higher spins. We show that, for large particle numbers, a spin-squeezing parameter for entanglement detection based on one of our inequalities is strictly stronger than the original spin-squeezing parameter defined in S\o{}rensen et al. [Nature (London) 409, 63 (2001)]. We present a coordinate system independent form of our inequalities that contains, besides the correlation and covariance tensors of the collective angular momentum operators, the nematic tensor appearing in the theory of spin nematics. Finally, we discuss how to measure the quantities appearing in our inequalities in experiments.

arXiv:1310.2269•Physical Review A•Mar 7, 2014•78 citations

Generalized spin squeezing criteria: Entanglement detection with collective measurements

Géza Tóth, Christian Knapp, Otfried Gühne +2 more

What is the relation between spin squeezing and entanglement? To clarify this, we derive the full set of generalized spin squeezing inequalities for the detection of entanglement. These are inequalities for the mean values and variances of the collective angular momentum components. They can be used for the experimental detection of entanglement in a system of spin‐12 particles in which the spins cannot be individually addressed. We also show how to obtain the complete set of entanglement conditions if the mean spin and the spin correlation matrix are known. Finally, we apply our criteria for entanglement detection in spin models, showing that they can be used to detect bound entanglement in the thermal state of these systems.

AIP conference proceedings•Jan 1, 2009•0 citations

Spin Squeezing Inequalities for Arbitrary Spin

Giuseppe Vitagliano, Philipp Hyllus, I. L. Egusquiza +1 more

We determine the complete set of generalized spin squeezing inequalities, given in terms of the collective angular momentum components, for particles with an arbitrary spin. They can be used for the experimental detection of entanglement in an ensemble in which the particles cannot be individually addressed. We also present a large set of criteria involving collective observables different from the angular momentum coordinates. We show that some of the inequalities can be used to detect k-particle entanglement and bound entanglement.

arXiv:1104.3147•Physical Review Letters•Dec 9, 2011•103 citations

Spin Squeezing and Quantum Correlations

A. R. Usha Devi, Sudha

Recent years have witnessed revolutionary improvement in the production, manipulation, characterization and quantification of multiatom (multiqubit) states - because of their promising applications in high precision atomic clocks, atomic interferrometry, quantum metrology and quantum information protocols. In the characterization and quantification of non-classical atomic correlations, two concepts namely, spin squeezing and quantum entanglement emerge. While spin squeezing originates from the uncertainty relation between atomic collective angular momentum operators, entanglement is a peculiar phenomena arising due to superpositions in the multiparticle Hilbert space. Here, we outline different quantitative measures of spin squeezing and discuss the intrinsic relation of spin squeezing with quantum entanglement in multiqubit systems.

arXiv:1101.0308•Dec 31, 2010•0 citations

Collective Randomized Measurements in Quantum Information Processing

Satoya Imai, Géza Tóth, Otfried Gühne

The concept of randomized measurements on individual particles has proven to be useful for analyzing quantum systems and is central for methods like shadow tomography of quantum states. We introduce collective randomized measurements as a tool in quantum information processing. Our idea is to perform measurements of collective angular momentum on a quantum system and actively rotate the directions using simultaneous multilateral unitaries. Based on the moments of the resulting probability distribution, we propose systematic approaches to characterize quantum entanglement in a collective-reference-frame-independent manner. First, we show that existing spin-squeezing inequalities can be accessible in this scenario. Next, we present an entanglement criterion based on three-body correlations, going beyond spin-squeezing inequalities with two-body correlations. Finally, we apply our method to characterize entanglement between spatially separated two ensembles.

arXiv:2309.10745•Physical Review Letters•Aug 8, 2024•16 citations
How can we analyze quantum correlations in large and noisy systems without quantum state tomography? An established method is to measure total angular momenta and employ the so-called spin-squeezing inequalities based on their expectations and variances. This allows detection of metrologically useful entanglement, but efficient strategies for estimating such nonlinear quantities have yet to be determined. In this paper we show that spin-squeezing inequalities can not only be evaluated by measurements of the total angular momentum but also by two-qubit correlations, either involving all pair correlations or randomly chosen pair correlations. Then we analyze the estimation errors of our approaches in terms of a hypothesis test. For this purpose, we discuss how error bounds can be derived for nonlinear estimators with the help of their variances, characterizing the probability of falsely detecting a separable state as entangled. We focus on the spin-squeezing inequalities in multiqubit systems. Our methods, however, can also be applied to spin-squeezing inequalities for qudits or for the statistical treatment of other nonlinear parameters of quantum states.
What is the relation between spin squeezing and entanglement? To clarify this, we derive the full set of generalized-spin-squeezing inequalities for the detection of entanglement. These are inequalities for the mean values and variances of the collective angular-momentum components Jk{J}_{k}Jk​. They can be used for the experimental detection of entanglement in a system of spin-12\frac{1}{2}21​ particles in which the spins cannot be individually addressed. We present various sets of inequalities that can detect all entangled states that can be detected based on the knowledge of (i) the mean values and variances of Jk{J}_{k}Jk​ in three orthogonal directions, or (ii) the variances of Jk{J}_{k}Jk​ in three orthogonal directions, or (iii) the mean values of Jk2{J}_{k}^{2}Jk2​ in three orthogonal directions, or (iv) the mean values and variances of Jk{J}_{k}Jk​ in arbitrary directions. We compare our inequalities to known spin-squeezing entanglement criteria and discuss to which extent spin squeezing is related to entanglement in the reduced two-qubit states. Finally, we apply our criteria for the detection of entanglement in spin models, showing that they can be used to detect bound entanglement in these systems.
A complete set of generalized spin-squeezing inequalities is derived for an ensemble of particles with an arbitrary spin. Our conditions are formulated with the first and second moments of the collective angular momentum coordinates. A method for mapping the spin-squeezing inequalities for spin-12\frac{1}{2}21​ particles to entanglement conditions for spin-jjj particles is also presented. We apply our mapping to obtain a generalization of the original spin-squeezing inequality to higher spins. We show that, for large particle numbers, a spin-squeezing parameter for entanglement detection based on one of our inequalities is strictly stronger than the original spin-squeezing parameter defined in S\o{}rensen et al. [Nature (London) 409, 63 (2001)]. We present a coordinate system independent form of our inequalities that contains, besides the correlation and covariance tensors of the collective angular momentum operators, the nematic tensor appearing in the theory of spin nematics. Finally, we discuss how to measure the quantities appearing in our inequalities in experiments.
What is the relation between spin squeezing and entanglement? To clarify this, we derive the full set of generalized spin squeezing inequalities for the detection of entanglement. These are inequalities for the mean values and variances of the collective angular momentum components. They can be used for the experimental detection of entanglement in a system of spin‐12 particles in which the spins cannot be individually addressed. We also show how to obtain the complete set of entanglement conditions if the mean spin and the spin correlation matrix are known. Finally, we apply our criteria for entanglement detection in spin models, showing that they can be used to detect bound entanglement in the thermal state of these systems.
We determine the complete set of generalized spin squeezing inequalities, given in terms of the collective angular momentum components, for particles with an arbitrary spin. They can be used for the experimental detection of entanglement in an ensemble in which the particles cannot be individually addressed. We also present a large set of criteria involving collective observables different from the angular momentum coordinates. We show that some of the inequalities can be used to detect k-particle entanglement and bound entanglement.
Recent years have witnessed revolutionary improvement in the production, manipulation, characterization and quantification of multiatom (multiqubit) states - because of their promising applications in high precision atomic clocks, atomic interferrometry, quantum metrology and quantum information protocols. In the characterization and quantification of non-classical atomic correlations, two concepts namely, spin squeezing and quantum entanglement emerge. While spin squeezing originates from the uncertainty relation between atomic collective angular momentum operators, entanglement is a peculiar phenomena arising due to superpositions in the multiparticle Hilbert space. Here, we outline different quantitative measures of spin squeezing and discuss the intrinsic relation of spin squeezing with quantum entanglement in multiqubit systems.
The concept of randomized measurements on individual particles has proven to be useful for analyzing quantum systems and is central for methods like shadow tomography of quantum states. We introduce collective randomized measurements as a tool in quantum information processing. Our idea is to perform measurements of collective angular momentum on a quantum system and actively rotate the directions using simultaneous multilateral unitaries. Based on the moments of the resulting probability distribution, we propose systematic approaches to characterize quantum entanglement in a collective-reference-frame-independent manner. First, we show that existing spin-squeezing inequalities can be accessible in this scenario. Next, we present an entanglement criterion based on three-body correlations, going beyond spin-squeezing inequalities with two-body correlations. Finally, we apply our method to characterize entanglement between spatially separated two ensembles.