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Steering Bell-diagonal states.

Quan Quan1, Huangjun Zhu2,3, Si-Yuan Liu1

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We found that Bell-diagonal states are steerable by two projective measurements if they violate the Clauser-Horne-Shimony-Holt (CHSH) inequality. This challenges expected hierarchies between quantum steering and Bell nonlocality.

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Area of Science:

  • Quantum Information Science
  • Quantum Foundations
  • Quantum Many-Body Systems

Background:

  • Quantum steering is a non-classical correlation where one party can influence the quantum state of another.
  • Bell-diagonal states are a fundamental class of two-qubit states with applications in quantum information processing.

Purpose of the Study:

  • To investigate the conditions for steerability of two-qubit Bell-diagonal states under projective measurements.
  • To establish a criterion for steerability and explore its relationship with Bell nonlocality.

Main Methods:

  • Analysis of the steering problem via its connection to joint-measurement problems.
  • Derivation of a necessary and sufficient criterion for steerability.
  • Introduction of a steering measure and its relation to concurrence and steering ellipsoid volume.

Main Results:

  • A Bell-diagonal state is steerable by two projective measurements if and only if it violates the Clauser-Horne-Shimony-Holt (CHSH) inequality.
  • This finding contrasts with the expected hierarchy between steering and Bell nonlocality.
  • A sufficient criterion for steerability under three projective measurements was derived, detecting more steerable states.

Conclusions:

  • The study provides a complete solution for the steerability of two-qubit Bell-diagonal states under two projective measurements.
  • It reveals a direct link between steerability and CHSH inequality violation, challenging established quantum information hierarchies.
  • The findings offer insights into entanglement, steering, and Bell nonlocality relationships.