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Generalized Quantum Measurements on a Higher-Dimensional System via Quantum Walks.
Xiaowei Wang1, Xiang Zhan2,3, Yulin Li2
1Beijing Computational Science Research Center, Beijing 100084, China.
Physical Review Letters
|October 28, 2023
Summary
Researchers developed a new method for generalized quantum measurements on higher-dimensional systems using quantum walks. This technique enables high-fidelity implementation of symmetric, informationally complete (SIC) positive-operator valued measurements (POVMs) for quantum information tasks.
Area of Science:
- Quantum mechanics
- Quantum information science
Background:
- Generalized quantum measurements are crucial for extracting information from quantum systems.
- Implementing these measurements on higher-dimensional quantum systems presents significant challenges.
Purpose of the Study:
- To propose a practical method for realizing general positive-operator valued measurements (POVMs) on higher-dimensional quantum systems.
- To experimentally demonstrate a symmetric, informationally complete (SIC) POVM on a three-dimensional system.
Main Methods:
- Utilizing a one-dimensional discrete-time quantum walk with a two-dimensional coin to implement general POVMs.
- Employing single photons and linear optics for experimental realization.
- Applying the SIC-POVM for qutrit state tomography.
Main Results:
- A simple recipe for implementing general POVMs on higher-dimensional systems was proposed.
- A high-fidelity experimental realization of a SIC-POVM on a three-dimensional system was achieved using single photons and linear optics.
- Qutrit state tomography using the SIC-POVM demonstrated infidelity scaling comparable to mutually unbiased bases.
Conclusions:
- The proposed method provides a viable approach for generalized quantum measurements in higher-dimensional systems.
- This work facilitates further exploration of quantum physics and information in higher dimensions.
- The developed technique has potential applications in quantum information processing tasks requiring generalized measurements.
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