Negative quantum conditional entropy and the entanglement measure of a kind of mixed state of bipartite quantum system

Abstract

From negative quantum conditional entropy point of view this paper intestigates the entanglement measure of the prue state and a kind of mixed state of bipartite quantum system. Also this paper gives a definition of quantum conditional entropy of entanglement EA｜B(ρAB) and proves that it satisfies the four fundamental conditions of a entanglement measure for a kind of mixed state of 2×2 quantum system by this negative quantum conditional entropy Using conditional entropy of entanglement, this paper investigates the quantum entanglement between the two identical two-level atoms simultaneously interacting with vacuum cavity field as an application. This paper compares conditional entropy of entanglement and concurrence at the same condition, and the result shows that the curves of their evolvements are identical. These obtained results test and verifys that conditions of an entanglement measure may be taken as the entanglement measure of the prue state and a kind of mixed state of bipartite quantum system.

Entanglement witness via quantum-memory-assisted entropic uncertainty relation

“…The extra term S (A|B) appearing on the right-hand side (RHS) is that of the joint state ρ AB before measurement. Note that the negative conditional von Neumann entropy S (A|B) is a signature of entanglement [18,19,[37][38][39], which is related to the quant um nonseparability [40] and the violation of entropic Bell inequalities [41]. Hence, the term S (A|B) can be used as a witnessing entanglement between the particle and the memory; this is our main purpose in this work.…”