ROMAN GIELERAK

University of Zielona Gora, Poland

Title: Renormalized form of the quantum von Neumann entropy for describing the entanglement in bipartite infinite dimensional systems

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Biography

Abstract

A renormalized version of the von Neumann quantum entropy ( which is finite and continuous in general, infinite dimensional case) and which obeys several of the natural physical demands ( as expected for a “good” measure of entanglement in the case of general quantum states describing bipartite and infinite-dimensional systems ) is proposed. The renormalized quantum entropy is defined by the explicite use of the Fredholm determinants theory. To prove the main results on the continuity and finiteness of the introduced renormalization the fundamental Grothendick approach, which is based on the infinite dimensional Grassmann algebra theory, is applied. Several features of majorization theory are preserved under the introduced renormalization as it is proved in this paper. This fact enables us to extend most of the known ( mainly, in the context of two-partite, finite-dimensional quantum systems )results of the LOCC comparison theory to the case of genuine infinite-dimensional , two-partite quantum systems.