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Quantifying Einstein-Podolsky-Rosen steering.

Paul Skrzypczyk1, Miguel Navascués2, Daniel Cavalcanti1

  • 1ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain.

Physical Review Letters
|May 27, 2014
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Summary
This summary is machine-generated.

We introduce a quantitative measure for Einstein-Podolsky-Rosen steering, a quantum correlation. Our findings reveal that all pure entangled states are maximally steerable, advancing quantum information science.

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Area of Science:

  • Quantum Information Science
  • Quantum Foundations
  • Quantum Correlations

Background:

  • Einstein-Podolsky-Rosen (EPR) steering is a unique quantum correlation between two parties, distinct from entanglement and Bell nonlocality.
  • EPR steering is crucial for entanglement certification with untrusted parties and has applications in quantum key distribution.
  • A quantitative measure for EPR steering has been lacking, hindering a deeper understanding and application of this phenomenon.

Purpose of the Study:

  • To develop a method for quantifying Einstein-Podolsky-Rosen steering.
  • To investigate the steerability of various quantum states using the proposed quantification.
  • To explore the relationship between EPR steering and other quantum phenomena like entanglement and Bell nonlocality.

Main Methods:

  • Proposed a novel mathematical framework to quantify the degree of Einstein-Podolsky-Rosen steering.
  • Analyzed the steerability of different quantum states, including pure entangled states and states with positive partial transposition.
  • Investigated specific examples of one-way steering and maximally steerable states.

Main Results:

  • Demonstrated that every pure entangled state exhibits maximal steerability.
  • Showed that the projector onto the antisymmetric subspace is maximally steerable across all dimensions.
  • Identified a new instance of one-way steering and provided evidence that states with positive partial transposition are not steerable.

Conclusions:

  • The proposed quantification provides a robust tool for characterizing EPR steering.
  • Pure entangled states and specific operators possess maximal steerability, offering insights into the nature of quantum correlations.
  • The findings contribute to a better understanding of the boundaries between entanglement, steering, and nonlocality, with implications for quantum technologies.