Entanglement in probability representation of quantum states and tomographic criterion of separability
Vladimir I. Man’ko, Giuseppe Marmo, E. C. G. Sudarshan, F. Zaccaria · Journal of Optics B Quantum and Semiclassical Optics · 2004
Entangled and separable states of a bipartite (multipartite) system are studied in the tomographic representation of quantum states. Properties of tomograms (joint probability distributions) corresponding to entangled states are discussed. The connection with star-product quantization is presented. U(N)-tomography and spin tomography as well as the relation of the tomograms to positive and completely positive maps are considered. The tomographic criterion of separability (necessary and sufficient condition) is formulated in terms of the equality of the specific function depending on unitary group parameters and positive map semigroup parameters to unity. Generalized Werner states are used as an example.