**A few open problems in quantum information**

Quantum information science, an interface area of mathematics,physics and computing science, is concerned with the manipulation, computation and communication of information, where the information is encoded in two (or more) level quantum systems called "qubits", unlike classical information, which is encoded in Boolean "bits". The devices used in this science are governed by the principles of quantum mechanics, which opens the possibility for a large range of applications. In this talk I will discuss several open problems in the field, focusing on the long standing additivity conjecture that the minimum entropy output of a completely positive trace preserving linear map, as measured using the von Neumann entropy, is additive under taking tensor products. Despite the enormous effort by the most experts in the field during the last 12 years, this problem remained unsolved. Here I will present some recent progress and future directions. This talk is based on a joint work with N. R. Wallach and A. Roy.