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Complete Hierarchy for High-Dimensional Steering Certification.

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We developed a method to certify high-dimensional entanglement in quantum steering. This procedure quantifies entanglement dimension and improves noise robustness for experimental certification.

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Area of Science:

  • Quantum Information Science
  • Quantum Entanglement
  • Quantum Foundations

Background:

  • High-dimensional quantum steering tests entanglement dimensionality without full device characterization.
  • It is crucial for quantum information protocols utilizing high-dimensional entanglement.
  • Experimental observations exist, but a general certification procedure is missing.

Purpose of the Study:

  • To provide necessary and sufficient conditions for certifying entanglement dimension in steering scenarios.
  • To develop a general certification procedure for high-dimensional quantum steering.
  • To quantify the phenomenon using steering dimension robustness.

Main Methods:

  • Formulated conditions as a hierarchy of semidefinite programs.
  • Applied the method to steering scenarios with maximally entangled states and mutually unbiased bases.
  • Characterized entanglement dimensionality in experimental setups.

Main Results:

  • Established a general certification procedure for high-dimensional quantum steering.
  • Developed a method to quantify entanglement dimension and its robustness.
  • Demonstrated practical viability and improved noise robustness bounds.

Conclusions:

  • The proposed method provides a robust way to certify high-dimensional entanglement in steering scenarios.
  • It enhances the experimental feasibility of utilizing high-dimensional entanglement in quantum technologies.
  • Offers stronger bounds on noise resilience for experimental certification.