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Published on: September 23, 2021
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Tapping into Permutation Symmetry for Improved Detection of k-Symmetric Extensions
Youning Li1, Chao Zhang2, Shi-Yao Hou3
1College of Science, China Agricultural University, Beijing 100080, China.
Entropy (Basel, Switzerland)
|October 28, 2023
Summary
This study introduces a new method leveraging permutation symmetry to improve the efficiency of symmetric extensions in quantum mechanics. The approach significantly reduces computational complexity for generalized qudit systems.
Area of Science:
- Quantum Information Theory
- Quantum Mechanics
- Mathematical Physics
Background:
- Symmetric extensions are crucial for analyzing entangled quantum systems and the quantum marginal problem.
- Semi-definite programming (SDP) is used for symmetric extensions but faces computational challenges with large parameter spaces in generalized qudit systems.
Purpose of the Study:
- To develop a computationally efficient method for detecting k-symmetric extensions in quantum systems.
- To reduce the dimensionality and parameter requirements for positive-definiteness tests in SDP.
Main Methods:
- Leveraging permutation symmetry to fine-tune semi-definite programming (SDP) problems.
- Developing an algorithm specifically for detecting k-symmetric extensions.
Main Results:
- Reduced algorithmic complexity from O(d^2k) to O(kd^2) for qudit k-symmetric extensions.
- Diminished search space dimensionality and the number of parameters for positive-definiteness tests.
- Streamlined verification of positive definiteness for SDP results.
Conclusions:
- The new approach offers significant algorithmic enhancements for studying symmetric extensions.
- This work provides a more efficient pathway for investigating quantum correlations and advancing quantum information theory.
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