Entanglement or separability: the choice of how to factorize the algebra of a density matrix

Author(s)
Walter Thirring, Reinhold Bertlmann, Philipp Köhler, Heide Narnhofer
Abstract

Quantum entanglement has become a resource for the fascinating developments in quantum information and quantum communication during the last decades. It quantifies a certain nonclassical correlation property of a density matrix representing the quantum state of a composite system. We discuss the concept of how entanglement changes with respect to different factorizations of the algebra which describes the total quantum system. Depending on the considered factorization a quantum state appears either entangled or separable. For pure states we always can switch unitarily between separability and entanglement, however, for mixed states a minimal amount of mixedness is needed. We discuss our general statements in detail for the familiar case of qubits, the GHZ states, Werner states and Gisin states, emphasizing their geometric features. As theorists we use and play with this free choice of factorization, which for an experimentalist is often naturally fixed. For theorists it offers an extension of the interpretations and is adequate to generalizations, as we point out in the examples of quantum teleportation and entanglement swapping.

Organisation(s)
Mathematical Physics, Particle Physics
Journal
European Physical Journal D
Volume
64
Pages
181-196
No. of pages
16
ISSN
1434-6060
DOI
https://doi.org/10.1140/epjd/e2011-20452-1
Publication date
2011
Peer reviewed
Yes
Austrian Fields of Science 2012
103036 Theoretical physics, 103019 Mathematical physics
Portal url
https://ucrisportal.univie.ac.at/en/publications/b1fda8af-340c-4f4c-a48d-c516af9ade62