Rostock 2019 – wissenschaftliches Programm
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Q: Fachverband Quantenoptik und Photonik
Q 59: Quantum Information (Concepts and Methods) V
Q 59.2: Vortrag
Freitag, 15. März 2019, 10:45–11:00, S HS 001 Chemie
Generalization of the Schmidt decomposition for bipartite systems — •Jens Siewert1,2 and Christopher Eltschka3 — 1University of the Basque Country UPV/EHU, E-48080 Bilbao, Spain — 2IKERBASQUE - Basque Foundation for Science, E-48013 Bilbao, Spain — 3Institut für Theoretische Physik, Universität Regensburg, D-93053 Regensburg
There are few mathematical statements in the quantum information toolbox that are as powerful and of ubiquitous applicability as the Schmidt decomposition. In words, it states that any pure state of a finite-dimensional two-party Hilbert space can be written in terms of a basis whose vectors are tensor products of elements of two orthonormal local bases, and its coefficients with respect to this basis are real.
In this contribution we discuss a straightforward extension of the Schmidt decomposition that apparently is not widely known. It amounts to a simultaneous decomposition of two pure states into four inter-related local bases. The price to pay for the simultaneous decomposition is the orthogonality of the bases or/and real-valuedness of the cofficients.