Parallelized projective measurements for spatial photonic qudits estimation

Area of Science:

• Quantum information science
• Quantum optics
• Quantum state reconstruction

Background:

• Quantum state tomography is crucial for characterizing quantum systems.
• Reconstructing high-dimensional quantum states (qudits) is challenging due to the exponential increase in measurement settings.
• Existing methods often require a large number of experimental settings, limiting practical applications.

Purpose of the Study:

• To develop a novel quantum state tomography method for arbitrary d-dimensional quantum states.
• To reduce the number of required experimental settings for efficient state reconstruction.
• To demonstrate the method's efficacy for high-dimensional photonic states.

Main Methods:

• Utilized a family of bases enabling spatially multiplexed projective measurements.
• Developed a method requiring only d+1 experimental settings for d-dimensional state reconstruction.
• Implemented the scheme for experimental reconstruction of 6-dimensional photonic states.

Main Results:

• Achieved high-fidelity reconstruction (above 0.97) for both pure and mixed d-dimensional states.
• Successfully reconstructed 6-dimensional quantum states where complete sets of mutually unbiased bases do not exist.
• Reduced the number of experimental settings from 42 to 7 for d=6 states.

Conclusions:

• The proposed quantum state tomography method is highly efficient for reconstructing high-dimensional quantum states.
• This technique overcomes limitations of previous methods, particularly for dimensions lacking complete mutually unbiased bases.
• The method offers a significant advancement for practical quantum information processing and quantum state characterization.