Liouville space explained

In the mathematical physics of quantum mechanics, Liouville space, also known as line space, is the space of operators on Hilbert space. Liouville space is itself a Hilbert space under the Hilbert-Schmidt inner product.^[1]

Abstractly, Liouville space is equivalent (isometrically isomorphic) to the tensor product of a Hilbert space with its dual.^{[2] [3]} A common computational technique to organize computations in Liouville space is vectorization.

Liouville space underlies the density operator formalism and is a common computation technique in the study of open quantum systems.

References

1. Fundamentals of quantum mechanics in Liouville space. Jerryman A.. Gyamfi. 16 October 2020. European Journal of Physics. 41. 6. 063002. 10.1088/1361-6404/ab9fdd. 2003.11472. 2020EJPh...41f3002G .
2. Web site: Hilbert space. Uni Hamburg. 29 Oct 2014. https://web.archive.org/web/20141029053526/https://www.chemie.uni-hamburg.de/nmr/insensitive/tutorial/en.lproj/hilbert_space.html. 24 April 2022.
3. Elementary open quantum states. Janos Polonyi. Ines. Rachid. Symmetry. 2021 . 13 . 9 . 1624 . 10.3390/sym13091624 . 2106.01443v2. 2021Symm...13.1624P . free .