Mainz 2026 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 67: Poster – Quantum Information

Q 67.30: Poster

Thursday, March 5, 2026, 17:00–19:00, Philo 2. OG

Quantum states on hyper-spheres — •Christian Schaub and Reinhold Walser — Institute for Applied Physics, TU Darmstadt, Germany

Quantum entanglement is a key resource in today’s quantum technologies, making its reliable quantification fundamentally important. A powerful strategy for characterizing entanglement is to decompose a quantum state into its local building blocks and compare these components with the original state, naturally connecting to the underlying geometry of quantum states [1]. While the Schmidt decomposition provides a perfect factorization, it only applies to pure states.

In this contribution, decomposition-based methods are therefore introduced for the analysis of arbitrary mixed states, with the Cholesky decomposition as a central element. The Cholesky decomposition provides a unique and compact factorization of density matrices and serves as the foundation for a hyper-spherical representation, in which quantum states can be interpreted as points on the surface of a hyper-sphere. Within this framework, entanglement can be understood as the geodesic distance on the hyper-sphere between the original state and the nearest separable state on the submanifold. This distance is minimized to quantify entanglement, yielding a closer separable approximation than partial-trace-based factorizations.

[1] Ingemar Bengtsson et al. Geometry of Quantum States: An Introduction to Quantum Entanglement. 2nd ed. Cambridge University Press, 2017

Keywords: Entanglement; Density matrix; Cholesky decomposition; Hyper-sphere