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Related Experiment Videos

Entanglement cost under positive-partial-transpose-preserving operations.

K Audenaert1, M B Plenio, J Eisert

  • 1QOLS, Blackett Laboratory, Imperial College of Science, Technology and Medicine, London, SW7 2BW, United Kingdom.

Physical Review Letters
|February 7, 2003
PubMed
Summary

We reveal the entanglement cost under quantum operations that preserve the positivity of the partial transpose (PPT operations). This cost is linked to logarithmic negativity, offering an operational interpretation for this entanglement measure.

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Area of Science:

  • Quantum Information Theory
  • Quantum Entanglement

Background:

  • Entanglement is a key resource in quantum information processing.
  • Quantifying entanglement and understanding its manipulation under specific quantum operations are crucial.
  • Positivity of the partial transpose (PPT) operations form a significant class of quantum operations.

Purpose of the Study:

  • To investigate the entanglement cost under PPT operations.
  • To establish an operational interpretation for entanglement measures.
  • To explore the relationship between different entanglement measures for specific quantum states.

Main Methods:

  • Analysis of entanglement cost under PPT operations.
  • Relating entanglement cost to logarithmic negativity.
  • Case studies on Werner states and Gaussian states.

Related Experiment Videos

  • Proving the coincidence of PPT cost and PPT entanglement of distillation for antisymmetric Werner states.

    • Main Results:

    • The entanglement cost under PPT operations is directly related to logarithmic negativity.
    • Logarithmic negativity is operationally interpreted as the entanglement cost for PPT operations.
    • For antisymmetric Werner states, PPT cost and PPT entanglement of distillation coincide.
    • Antisymmetric Werner states represent the first truly mixed states with asymptotically reversible entanglement manipulation under PPT operations.

    Conclusions:

    • Logarithmic negativity provides a fundamental operational measure for entanglement under PPT operations.
    • The coincidence of PPT cost and PPT entanglement of distillation for antisymmetric Werner states highlights a unique entanglement measure under PPT operations.
    • This finding advances the understanding of entanglement manipulation and its reversibility for mixed quantum states.