Research Paper#Quantum Information Theory, Entanglement, Singular Value Decomposition🔬 ResearchAnalyzed: Jan 3, 2026 16:17
Generalized Entanglement Entropies via Unit-Invariant SVD
Published:Dec 28, 2025 16:51
•1 min read
•ArXiv
Analysis
This paper introduces novel generalizations of entanglement entropy using Unit-Invariant Singular Value Decomposition (UISVD). These new measures are designed to be invariant under scale transformations, making them suitable for scenarios where standard entanglement entropy might be problematic, such as in non-Hermitian systems or when input and output spaces have different dimensions. The authors demonstrate the utility of UISVD-based entropies in various physical contexts, including Biorthogonal Quantum Mechanics, random matrices, and Chern-Simons theory, highlighting their stability and physical relevance.
Key Takeaways
- •Introduces generalized entanglement entropies based on UISVD.
- •These entropies are invariant under scale transformations.
- •Applicable to non-Hermitian operators and rectangular operators.
- •Demonstrated in various physical contexts, including Biorthogonal Quantum Mechanics.
- •Yields stable and physically meaningful entropic spectra.
Reference
“The UISVD yields stable, physically meaningful entropic spectra that are invariant under rescalings and normalisations.”