Separability and distillability of bipartite Gaussian states -- the complete story (Q2767555)

Quantum information theory (QIT) is a new field of science where the processing of quantum information (QI) and communication play the important role. Here a notion of quantum entanglement (QET) keeps the crucial position. For a definition and description of QET one needs to understand a separability criterion of quantum states. Then for a processing of QET one needs to have pure entangled states. The process of getting such states from noisy entangled states is called a distillation. Let us stress here that in general for more than two entangled states both mentioned problems are unsolved yet. So every little step in this direction is of importance in building QIT, to be used, e.g., for quantum computing. NEWLINENEWLINENEWLINEThe problem of separability and distillability treated in this paper is solved for a special case of bipartite Gaussian states. By other words, necessary and sufficient conditions are formulated for two systems \(A\) and \(B\), composed of \(n\) and \(m\) modes respectively, in a Gaussian state, to be separable and distillable. Besides, it is shown that there are no so called bound entangled Gaussian states. So such states are distillable and thus useful for quantum communication.NEWLINENEWLINENEWLINEThe obtained result is important as Gaussian states are of particular interest, since most proposed applications in quantum communication are based on such states representing continuous variables case. Alas, for non-Gaussian states, however, both problems of separability and distillability remain open, representing two of great challenges of QIT.