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Quantification of Gaussian quantum steering.

Ioannis Kogias1, Antony R Lee1, Sammy Ragy1

  • 1School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.

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We introduce a computable measure for quantifying Einstein-Podolsky-Rosen (EPR) steering in quantum systems. This measure connects to quantum key distribution and confirms that steering bound entangled Gaussian states is impossible using Gaussian measurements.

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Area of Science:

  • Quantum Information Science
  • Quantum Correlations
  • Nonclassical Correlations

Background:

  • Einstein-Podolsky-Rosen (EPR) steering is a key quantum correlation between entanglement and Bell nonlocality.
  • Existing criteria for EPR steering are qualitative, lacking quantitative measures.
  • Quantifying steerability is crucial for understanding and utilizing quantum correlations.

Purpose of the Study:

  • To introduce a computable measure for quantifying steering in arbitrary bipartite Gaussian states.
  • To establish an operational link between steering quantification and quantum key distribution.
  • To investigate the possibility of steering bound entangled Gaussian states.

Main Methods:

  • Development of a computable measure for steering in continuous variable systems.
  • Analysis of the measure for two-mode Gaussian states, relating it to coherent information.
  • Investigation of the connection to one-sided device-independent quantum key distribution key rates.

Main Results:

  • A computable measure of steering for bipartite Gaussian states is introduced.
  • For two-mode Gaussian states, the measure equals coherent information, bounded by entanglement.
  • The measure is operationally linked to the key rate in one-sided device-independent quantum key distribution.
  • Peres' conjecture is proven in its stronger form for Gaussian states: steering bound entangled Gaussian states via Gaussian measurements is impossible.

Conclusions:

  • The developed measure provides a quantitative tool for assessing EPR steering in Gaussian quantum systems.
  • The findings deepen the understanding of the relationship between steering, entanglement, and quantum key distribution.
  • The impossibility of steering bound entangled Gaussian states with Gaussian measurements has been rigorously demonstrated within the Gaussian regime.