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Resource-Efficient High-Dimensional Entanglement Detection via Symmetric Projections
Simon Morelli1, Marcus Huber2, Armin Tavakoli3
1BCAM - Basque Center for Applied Mathematics, Mazarredo 14, 48009 Bilbao, Spain.
Physical Review Letters
|November 13, 2023
Summary
We developed new criteria to detect and measure quantum entanglement in bipartite states. These methods are efficient, noise-tolerant, and work for high-dimensional quantum systems.
Area of Science:
- Quantum Information Science
- Quantum Entanglement Theory
Background:
- Entanglement is a key resource in quantum information science.
- Detecting and quantifying entanglement in high-dimensional systems remains challenging.
Purpose of the Study:
- Introduce novel criteria for detecting and quantifying bipartite quantum state entanglement.
- Provide qualitative and quantitative measures of entanglement, applicable to arbitrary local dimensions.
Main Methods:
- Develop criteria based on measurements in mutually unbiased bases.
- Develop criteria based on equiangular measurements.
- Demonstrate universal applicability without prior state assumptions.
Main Results:
- Criteria yield entanglement dimension (qualitative) and fidelity with maximally entangled states (quantitative).
- Experimenters can tune resource-efficiency versus noise-tolerance by adjusting measurement count.
- Near-optimal detection is achievable with few measurements for common noise models.
- Global product projections scale linearly with local dimension, enabling high-dimensional entanglement analysis.
Conclusions:
- The proposed criteria offer a versatile and scalable approach for entanglement characterization.
- These methods facilitate the study and application of entanglement in complex quantum systems.
- The linear scaling of measurements paves the way for exploring very high-dimensional entanglement.
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