Abstarct: In information theory, amount of our information about a physical system is named information and theoretical scientists used concept of entropy for quantified it. Information can be classical or quantum. Classical information quantified by Shannon and quantum information quantifie by Neumann. Here we consider a bipartite system that it subsystems correlated together. Amount of required information for send total state of system to one of subsystems is named conditional information. Difference between classical systems and quantum systems is specified at kind of correlation between their subsystems. Subsystems of a quantum system can have a kind of correlation that is classically forbidden. This correlation is named entanglement. Unlike in classical information theory, quantum conditional entropy can be negative when considering quantum entangled systems. Here we introduce a quantum information theory that allows us for a consistent descxription of entanglement. Also we present that entanglement of quantum systems can be successfully described by negative quantum conditional entropies. Thereby we can verify the entanglement of a quantum system by quantum conditional entropy and quantum conditional density matrix.