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Quantifying entanglement in a 68-billion-dimensional quantum state space.

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Quantifying quantum entanglement in large systems is now feasible with limited data. Our new method drastically reduces measurement needs for high-dimensional entanglement, enabling advanced quantum information processing.

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Area of Science:

  • Quantum Information Science
  • Quantum Optics
  • Quantum Metrology

Background:

  • Quantum entanglement is a key resource for quantum information processing, enabling enhanced computing, simulation, communication, and metrology.
  • Precisely quantifying entanglement in unknown quantum states typically requires an intractable number of measurements, especially for high-dimensional systems.

Purpose of the Study:

  • To develop a rigorous method for quantifying high-dimensional entanglement using significantly reduced experimental data.
  • To demonstrate the effectiveness of this method on a system of two spatially entangled photons.

Main Methods:

  • An entropic, quantitative entanglement witness was adapted to operate directly on compressed experimental data.
  • An adaptive, multilevel sampling procedure was employed to acquire limited, targeted data.
  • The method was applied to certify the entanglement of formation for a high-dimensional photonic system.

Main Results:

  • Successfully quantified high-dimensional entanglement using only 6,456 measurements.
  • Certified an entanglement of formation of 7.11 ± 0.04 ebits for two spatially entangled photons.
  • Achieved a reduction of 20 million times fewer measurements compared to uncompressed data and 10^18 times fewer than full tomography for a system with over 68 billion dimensions.

Conclusions:

  • The developed technique provides a universal and efficient method for rigorously quantifying entanglement in large quantum systems shared by two parties.
  • This approach overcomes the measurement limitations of traditional methods, paving the way for practical applications in quantum information science.