Cauchy tensor and the classicality and separability condition of spin states

In this literature, we are concerned with the necessary condition for classicality and separability of the spin states by virtue of Cauthy tensors. The classicality and separability of the spin-j states are identified with the positive semidefiniteness of the 2j order associated tensor under tensor representation of quantum states. According to the properties of Bloch vector and trρ=1, we present necessary condition for classicality (separability) and entanglement of the spin-j states by virtue of Cauthy tensors with the positive generating vector c. This necessary condition not only perfectly maintains the physical properties of the quantum system, but also depends only on spin-j and the generating vector c. In addition, we show that Cauchy tensor method has a wider detection range and is easy to verify compared with the existing smallest tensor eigenvalue method. •We first investigate quantum classicality and entanglement in basis of Cauchy tensor.•The condition maintains physical properties and only depends on the generated vector.•Our method improve the smallest tensor eigenvalue method in terms of detection range.