**The global and local additivity problems in quantum information theory** - Shmuel Friedland

The capacity of the classical channel was investigated by Claude Shannon in 1948. This capacity is additive under the tensor products of two channels. The capacity of a quantum channel (QC) was introduced by Alexander Holevo in 1998. One of the fundamental problems in quantum information theory is whether the capacity of QC is additive or not under the tensor product. Equivalently, can entangled input increase the quantum capacity?
In 2009 Matthew Hastings gave a positive answer to this problem!
It was shown by Peter Shor in 2004 that the additivity of the Holevo capacity is equivalent to:
- additivity of the minimum entropy output of a quantum channel,
- additivity of the entanglement of formation,
- strong superadditivity of the entanglement of formation.
Contrary to the above result we will show that the local minimum entropy output of a quantum channel is additive. This result is a joint work with Gilad Gour.