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Related Experiment Video

Updated: Jul 13, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

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Published on: May 30, 2014

Inseparability criteria for continuous bipartite quantum states.

E Shchukin¹, W Vogel

¹Arbeitsgruppe Quantenoptik, Institut für Physik, Universität Rostock, D-18051 Rostock, Germany. evgeny.shchukin@uni-rostock.de

Physical Review Letters

|December 31, 2005

Summary

This summary is machine-generated.

We found conditions for bipartite harmonic quantum states to be nonnegative after partial transposition. Violating these conditions guarantees entanglement, encompassing prior entanglement criteria.

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Area of Science:

Quantum Information Theory
Quantum Many-Body Systems

Background:

Bipartite quantum states are fundamental in quantum information.
Entanglement detection in quantum systems is a key challenge.
Harmonic quantum states are a specific class of quantum states.

Purpose of the Study:

To establish necessary and sufficient conditions for the nonnegativity of partially transposed bipartite harmonic quantum states.
To develop a new framework for entanglement detection in these states.

Main Methods:

Formulation of conditions as an infinite series of inequalities involving moments of the quantum state.
Analysis of the relationship between state nonnegativity and entanglement.

Main Results:

Derived a complete set of inequalities for the partial transposition of bipartite harmonic quantum states.
Demonstrated that violation of any inequality in the series is a sufficient condition for entanglement.
Showcased that existing entanglement conditions are particular instances of the new approach.

Conclusions:

The developed conditions provide a powerful tool for identifying entanglement in bipartite harmonic quantum states.
This work unifies and generalizes previous entanglement detection methods.
The findings contribute to a deeper understanding of quantum correlations in harmonic systems.