Metrological Detection of Multipartite Entanglement from Young Diagrams

Abstract

We characterize metrologically useful multipartite entanglement by representing partitions with Young diagrams. We derive entanglement witnesses that are sensitive to the shape of Young diagrams and show that Dyson's rank acts as a resource for quantum metrology. Common quantifiers, such as the entanglement depth and $k$-separability are contained in this approach as the diagram's width and height. Our methods are experimentally accessible in a wide range of atomic systems, as we illustrate by analyzing published data on the quantum Fisher information and spin-squeezing coefficients.

6 + 7 pages, 5 + 8 figures

References in corpus (8)

• Entanglement detection
• 14-qubit entanglement: creation and coherence
• Quantum metrology from a quantum information science perspective
• Fisher Information and entanglement of non-Gaussian spin states
• Entanglement Certification $-$ From Theory to Experiment
• Scalable Spin Squeezing for Quantum-Enhanced Magnetometry with Bose-Einstein Condensates
• Multipartite entanglement in topological quantum phases
• Efficient entanglement criteria for discrete, continuous, and hybrid variables

Cited by in corpus (1)

• Characterizing Multipartite Non-Gaussian Entanglement for Three-Mode Spontaneous Parametric Down-Conversion Process