Five Measurement Bases Determine Pure Quantum States on Any Dimension

Area of Science:

• Quantum mechanics
• Quantum information science

Background:

• Determining the minimum observables for quantum state characterization is a fundamental problem.
• High-dimensional quantum information processing demands efficient state reconstruction methods.

Purpose of the Study:

• To establish the minimum number of observables for unambiguous reconstruction of pure quantum states.
• To develop a method applicable to high-dimensional systems.

Main Methods:

• Utilizing projective measurements onto five orthonormal bases.
• Demonstrating state reconstruction through a linear scaling of measurement outcomes (5d) with dimension (d).

Main Results:

• Any pure d-dimensional quantum state can be unambiguously reconstructed using five observables.
• The number of measurement outcomes scales linearly with dimension (5d).
• The reconstruction method is robust against experimental errors and requires simple postprocessing.

Conclusions:

• Five observables are sufficient for the complete characterization of any pure d-dimensional quantum state.
• The proposed method is experimentally feasible, as demonstrated with eight-dimensional states.
• This work provides a significant advancement for high-dimensional quantum information processing.