Creation Of Biseparable Criterions Based On The Relationship Among Density Matrix Entries

Quantum entanglement is an important character of quantum physics, and is also a newresource. So the study on the properties of quantum entanglement are becoming more and moreimportant. We use the density matrix entries of one dimensional four, five and six qubits Clusterstate to construct some necessary conditions of bi-separable quantum states. And then we obtaindifferent criterions with the similar methods, based on a kind of special quantum states whichare written as |ψ>n = 21(|0……0> + |001……1> + |110……0> > |1……1>). The main theorems weobtain are as follow:I is a string of 4 classical bits, I′is a string of 2 classical bits. if the inequality does not,ρisgenuine 4-partite entangled.where I is a string of 3 classical bits, I′and I′′are strings of 2 classical bits. If it goes againstthe inequality, thenρis genuine 5-partite entangled.and violation implies genuine 6-qubit entanglement. Here I and I′are strings of 6 classical bitsand 3 classical bits, respectively.