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:1504.06189

Criteria for particle entanglement in many-body systems of bosons

Tomasz Wasak, Piotr Szańkowski, Marek Trippenbach, Jan Chwedeńczuk

Published Apr 23, 2015• 0 citations
arXivHTMLPDF

Abstract

Basing on the analogy between the coherent states of light and separable states of $N$ bosons, we demonstrate that the violation Cauchy-Schwarz inequality for any-order correlation function signals the entanglement among the constituent particles. Rather than restricting to the correlations between the positions of particles, we consider the broadest set of measurements allowed by quantum mechanics. Our result is general -- it applies to any quantum system of bosons, even when the number of particles is not fixed, provided that there is no coherence between different number states. We also demonstrate that the compact expression for the separable state of bosons can be used to relate some known metrological quantities to the particle entanglement in a very simple way.

DOI
10.48550/arxiv.1504.06189

Related papers

Cauchy-Schwarz inequality and particle entanglement

Tomasz Wasak, Piotr Szańkowski, Paweł Zin +2 more

Recently, violation of the Cauchy-Schwarz inequality by the second-order correlation function was reported in a collection of ultracold bosons [Kheruntsyan et al., Phys. Rev. Lett. 108, 260401 (2012)]. We show that the observation of this effect proves the presence of particle entanglement in a many-body system of bosons. Our derivation is based on the analogy between the coherent states of electromagnetic fields and separable states of massive particles. The presented argument applies to any quantum system of identical bosons with either a fixed or a fluctuating number of particles, provided that there is no coherence between different number states.

arXiv:1311.3855•Physical Review A•Sep 17, 2014•28 citations

Role of Particle Entanglement in the Violation of Bell Inequalities

Tomasz Wasak, Augusto Smerzi, Jan Chwedeńczuk

Entanglement between two separate systems is a necessary resource to violate a Bell inequality in a test of local realism. We demonstrate that to overcome the Bell bound, this correlation must be accompanied by the entanglement between the constituent particles. This happens whenever a super-selection rule prohibits coherences between states with different total number of particles and thus imposes a constraint on feasible local operations in each sub-system. We show that the necessary entanglement between the particles might solely result from their indistinguishability. We also give an example of both mode and particle-entangled pure state, which does not violate any Bell inequality. Our result reveals a fundamental relation between the non-locality and the particle entanglement.

arXiv:1609.01576•Scientific Reports•Jan 23, 2018•13 citations

Mixed state entanglement via the Cauchy-Schwarz inequality

Nishaant Jacobus, Paul W. Brumer, Chern Chuang

The entanglement properties of mixed states are of great importance in the study of open quantum systems and quantum information science, but common entanglement criteria such as the Peres-Horodecki condition can be difficult to relate to physical properties of the system. We introduce the Cauchy-Schwarz violation (CSV) condition for entanglement, which has a simple dependence on the populations and coherences of the density operator. A sufficient condition for entanglement, it provides a direct connection to the physical characteristics of the system such as its symmetries, yielding intuition that can be used to understand and engineer highly entangled states. We illustrate the often surprising insights gained from the CSV condition by applying it to the Jaynes-Cummings model, the quantum Rabi model, and an open-system quantum Rabi model.

arXiv:2508.00334•Physical Review Research•Jul 6, 2026•0 citations

Unified approach to entanglement criteria using the Cauchy-Schwarz and Hölder inequalities

Sabine Wölk, Marcus Huber, Otfried Gühne

We present a unified approach to different recent entanglement criteria. Although they were developed in different ways, we show that they are all applications of a more general principle given by the Cauchy-Schwarz inequality. We explain this general principle and show how to use it to derive not only already known entanglement criteria, but also criteria which were unknown so far. We systematically investigate its potential and limitations to detect bipartite and multipartite entanglement. Furthermore, we describe how to apply our generalized entanglement detection scheme to find the measurement directions to verify the entanglement of a given state experimentally.

arXiv:1405.0986•Physical Review A•Aug 15, 2014•15 citations

General criterion for the entanglement of two indistinguishable particles

G. C. Ghirardi, Luca Marinatto

We relate the notion of entanglement for quantum systems composed of two identical constituents to the impossibility of attributing a complete set of properties to both particles. This implies definite constraints on the mathematical form of the state vector associated with the whole system. We then analyze separately the cases of fermion and boson systems, and we show how the consideration of both the Slater-Schmidt number of the fermionic and bosonic analog of the Schmidt decomposition of the global state vector and the von Neumann entropy of the one-particle reduced density operators can supply us with a consistent criterion for detecting entanglement. In particular, the consideration of the von Neumann entropy is particularly useful in deciding whether the correlations of the considered states are simply due to the indistinguishability of the particles involved or are a genuine manifestation of the entanglement. The treatment leads to a full clarification of the subtle aspects of entanglement of two identical constituents which have been a source of embarrassment and of serious misunderstandings in the recent literature.

arXiv:quant-ph/0401065•Physical Review A•Jul 22, 2004•290 citations

Bell-Type Inequalities to Detect True n -Body Nonseparability

Daniel Collins, Nicolas Gisin, Sandu Popescu +2 more

We analyze the structure of correlations among more than two quantum systems. We introduce a classification of correlations based on the concept of nonseparability, which is different a priori from the concept of entanglement. Generalizing a result of Svetlichny [Phys. Rev. D 35, 3066 (1987)] on three-particle correlations, we find an inequality for n-particle correlations that holds under the most general separability condition and that is violated by some quantum-mechanical states.

arXiv:quant-ph/0201058•Physical Review Letters•Apr 12, 2002•298 citations
Basing on the analogy between the coherent states of light and separable states of NNN bosons, we demonstrate that the violation Cauchy-Schwarz inequality for any-order correlation function signals the entanglement among the constituent particles. Rather than restricting to the correlations between the positions of particles, we consider the broadest set of measurements allowed by quantum mechanics. Our result is general -- it applies to any quantum system of bosons, even when the number of particles is not fixed, provided that there is no coherence between different number states. We also demonstrate that the compact expression for the separable state of bosons can be used to relate some known metrological quantities to the particle entanglement in a very simple way.
Recently, violation of the Cauchy-Schwarz inequality by the second-order correlation function was reported in a collection of ultracold bosons [Kheruntsyan et al., Phys. Rev. Lett. 108, 260401 (2012)]. We show that the observation of this effect proves the presence of particle entanglement in a many-body system of bosons. Our derivation is based on the analogy between the coherent states of electromagnetic fields and separable states of massive particles. The presented argument applies to any quantum system of identical bosons with either a fixed or a fluctuating number of particles, provided that there is no coherence between different number states.
Entanglement between two separate systems is a necessary resource to violate a Bell inequality in a test of local realism. We demonstrate that to overcome the Bell bound, this correlation must be accompanied by the entanglement between the constituent particles. This happens whenever a super-selection rule prohibits coherences between states with different total number of particles and thus imposes a constraint on feasible local operations in each sub-system. We show that the necessary entanglement between the particles might solely result from their indistinguishability. We also give an example of both mode and particle-entangled pure state, which does not violate any Bell inequality. Our result reveals a fundamental relation between the non-locality and the particle entanglement.
The entanglement properties of mixed states are of great importance in the study of open quantum systems and quantum information science, but common entanglement criteria such as the Peres-Horodecki condition can be difficult to relate to physical properties of the system. We introduce the Cauchy-Schwarz violation (CSV) condition for entanglement, which has a simple dependence on the populations and coherences of the density operator. A sufficient condition for entanglement, it provides a direct connection to the physical characteristics of the system such as its symmetries, yielding intuition that can be used to understand and engineer highly entangled states. We illustrate the often surprising insights gained from the CSV condition by applying it to the Jaynes-Cummings model, the quantum Rabi model, and an open-system quantum Rabi model.
We present a unified approach to different recent entanglement criteria. Although they were developed in different ways, we show that they are all applications of a more general principle given by the Cauchy-Schwarz inequality. We explain this general principle and show how to use it to derive not only already known entanglement criteria, but also criteria which were unknown so far. We systematically investigate its potential and limitations to detect bipartite and multipartite entanglement. Furthermore, we describe how to apply our generalized entanglement detection scheme to find the measurement directions to verify the entanglement of a given state experimentally.
We relate the notion of entanglement for quantum systems composed of two identical constituents to the impossibility of attributing a complete set of properties to both particles. This implies definite constraints on the mathematical form of the state vector associated with the whole system. We then analyze separately the cases of fermion and boson systems, and we show how the consideration of both the Slater-Schmidt number of the fermionic and bosonic analog of the Schmidt decomposition of the global state vector and the von Neumann entropy of the one-particle reduced density operators can supply us with a consistent criterion for detecting entanglement. In particular, the consideration of the von Neumann entropy is particularly useful in deciding whether the correlations of the considered states are simply due to the indistinguishability of the particles involved or are a genuine manifestation of the entanglement. The treatment leads to a full clarification of the subtle aspects of entanglement of two identical constituents which have been a source of embarrassment and of serious misunderstandings in the recent literature.