Priority Choice Experimental Two-Qubit Tomography: Measuring One by One All Elements of Density Matrices

Area of Science:

• Quantum Information Science
• Quantum Optics
• Experimental Physics

Background:

• Standard quantum tomography methods often amplify experimental data errors during density matrix (ρ) reconstruction.
• Indirect measurement of off-diagonal elements in ρ leads to error magnification in linear inversion techniques.

Purpose of the Study:

• To implement and experimentally validate a recently proposed optimal quantum tomography solution for two-qubit polarization states.
• To compare the performance and error stability of the optimal method against established tomographic protocols.

Main Methods:

• Experimental implementation of an optimal quantum tomography method measuring all density matrix (ρ) elements directly.
• Comparison with standard protocols using local measurements (Pauli operators, JWM projectors) and mutually unbiased bases (local and global measurements).
• Reconstruction of seventeen separable, partially, and maximally entangled two-qubit polarization states.

Main Results:

• The implemented optimal tomography method exhibits the highest stability against experimental errors compared to other protocols.
• Optimally reconstructed states are characterized by the smallest uncertainty circle radius, measured by trace distance and disturbance.
• Experimental estimation of uncertainty radii for all tomographies shows intersecting circles, indicating the approximate physical density matrix location.

Conclusions:

• The optimal quantum tomography method provides a more robust and accurate approach for reconstructing quantum states, particularly two-qubit states.
• This method significantly reduces error propagation, leading to more reliable characterization of quantum systems.
• The uncertainty circle analysis offers a valuable tool for assessing the fidelity and precision of quantum state reconstruction.