Direct measurement of a 27-dimensional orbital-angular-momentum state vector

Area of Science:

• Quantum Physics
• Quantum Information Science

Background:

• Quantum state measurement is experimentally challenging.
• Direct measurement offers in situ characterization via sequential weak and strong measurements.
• Existing methods are limited, particularly for high-dimensional states.

Purpose of the Study:

• To demonstrate the practical direct measurement of a high-dimensional quantum state vector.
• To utilize orbital angular momentum as a discrete basis for high-dimensional states.
• To extend direct measurement capabilities beyond polarization states.

Main Methods:

• Employed sequential weak measurements of orbital angular momentum.
• Utilized strong measurements of angular position.
• Applied the technique to a pure state with dimensionality d=27.

Main Results:

• Successfully performed direct measurement of a high-dimensional state vector (d=27).
• Measured the complex probability amplitudes of the quantum state.
• Directly observed the relationship between state vector rotations and relative phase of orbital angular momentum components.

Conclusions:

• The developed technique enables practical direct measurement of high-dimensional quantum states.
• This method is crucial for advancing high-dimensional classical and quantum information systems.
• The technique is adaptable for characterizing other complex quantum states.