Von neumann entropy as information rate

Richard Jozsa

Dėnes Petz

Bijan Nikouravan

The Von Neumann entropy plays a central role in the quantum information theory and is a concave function and following the property . In this paper, we introduce a new proof for the linearity of Von Neumann entropy in the rate without using the above inequality. Here the Von Neumann entropy is concave; that is, given weights and density matrices . Roughly speaking, we will show that in the rate case, the Von Neumann entropy is linear without using Fannes inequality. https://orcid.org/0000-0003-4308-1632

Oliver Johnson, Yuri Suhov

A model of a quantum information source is proposed, based on the Gibbs ensemble of ideal (free) particles (bosons or fermions). We identify the (thermodynamic) von Neumann entropy as the information rate and establish the classical Lempel--Ziv universal coding algorithm in Grassberger's form for such a source. This generalises the Schumacher theorem to the case of non-IID qubits.

Yuan Li, Paul Busch

Berry Schoenmakers, Jilles Tjoelker, Pim Tuyls +1 more

We prove that the average smooth Renyi entropy rate will approach the entropy rate of a stationary, ergodic information source, which is equal to the Shannon entropy rate for a classical information source and the von Neumann entropy rate for a quantum information source.