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Bound entanglement and continuous variables

Horodecki1, Lewenstein

  • 1Faculty of Applied Physics and Mathematics, Technical University of Gdansk, 80-952 Gdansk, Poland and Institute fur Theoretische Physik, Universitat Hannover, D-30167 Hannover, Germany.

Physical Review Letters
|September 16, 2000
PubMed
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We define generic bound entanglement for continuous variables and present new bound entangled states. These states have implications for quantum optics and can be detected using entanglement witnesses.

Area of Science:

  • Quantum Information Theory
  • Quantum Optics

Background:

  • Bound entanglement is a quantum resource that cannot be distilled into pure entanglement.
  • Continuous variable (CV) systems are crucial for quantum optics and quantum information processing.
  • Understanding generic entanglement is key to characterizing quantum states.

Purpose of the Study:

  • To introduce and define generic bound entanglement for continuous variable systems.
  • To explore the physical significance of these states in quantum optics.
  • To investigate the genericity of entanglement in newly identified bound entangled states.

Main Methods:

  • Development of a formal definition for generic bound entanglement in the context of continuous variables.
  • Construction and analysis of specific examples of bound entangled states for CV systems.

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  • Investigation of entanglement properties using entanglement witnesses and positive maps.

    • Main Results:

    • Introduction of the definition of generic bound entanglement for continuous variable systems.
    • Presentation of novel examples of bound entangled states with positive partial transpose.
    • Demonstration that entanglement witnesses and positive maps for these states are readily constructible.

    Conclusions:

    • The study establishes a framework for generic bound entanglement in continuous variable systems.
    • New families of bound entangled states with practical implications for quantum optics have been identified.
    • The developed methods facilitate the detection and characterization of bound entanglement in quantum systems.