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We developed new semidefinite programming methods to benchmark entanglement in high-dimensional quantum systems. These tools efficiently detect entanglement dimensionality and estimate source fidelity for quantum experiments.

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Area of Science:

  • Quantum Information Science
  • Quantum Optics
  • High-Dimensional Quantum Systems

Background:

  • Quantum entanglement is a key resource in quantum information science.
  • Characterizing entanglement in high-dimensional systems is experimentally challenging.
  • Existing methods for entanglement benchmarking can be computationally intensive.

Purpose of the Study:

  • To introduce novel semidefinite programming hierarchies for benchmarking entanglement properties.
  • To develop efficient methods for analyzing high-dimensional quantum steering scenarios.
  • To provide tools for experimental verification of quantum entanglement.

Main Methods:

  • Utilizing semidefinite programming hierarchies for entanglement benchmarking.
  • Developing a general method for detecting entanglement dimensionality via Schmidt number certification.
  • Implementing a method to estimate the fidelity of a quantum source with maximally entangled states.

Main Results:

  • A general method for detecting entanglement dimensionality with computational cost independent of the Schmidt number.
  • A method for estimating the fidelity of a quantum source with any maximally entangled state.
  • Demonstrated the practical utility of these methods for analyzing high-dimensional quantum experiments.

Conclusions:

  • The introduced semidefinite programming hierarchies offer efficient tools for characterizing quantum entanglement.
  • These methods are applicable to real-world experiments involving high-dimensional quantum systems.
  • The developed techniques advance the ability to benchmark and verify quantum entanglement properties.