Multipartite Entanglement: Classification, Quantification, Manipulation, Evolution and Applications

Exotic multipartite entangled states plays an important role in a variety of quantum information processing tasks such as conventional and measurement-based quantum computation, quantum error correction schemes, quantum secret sharing, quantum simulations, and in principle in the description of every composite system consisting of more than one subsystem. The amount of information needed to describe N-party quantum system grows exponentially with N, which makes it very difficult and almost impossible to classify multipartite entangled states. In this talk I will show that a new formalism based on the stabilizer group of a given multipartite state, not only makes it possible to classify and quantify the amount of entanglement in multipartite states, but also describes fully the manipulation of multipartite entanglement under separable operations. In particular, I will introduce necessary and sufficient conditions to transform one pure multipartite state to another multipartite state via separable operations. In addition, I will discuss the evolution of multipartite entanglement under noise and decoherence, and its quantification in terms of SL-invariant polynomials. I will end with few applications to quantum secret sharing. Some of the work presented here is based on a joint work with Nolan Wallach.