Fully Quantum Slepian Wolf and Decoupling Theorem

In this talk, we shall discuss the fully quantum Slepian Wolf theorem and it's proof (Winter et al). The input to the fully Quantum Slepian Wolf protocol is a tripartite state \psi^{ABR} and the output state is a state close to \psi^{RB'} \tensor \Phi^{A_2 B''}, where A=A_1 \tensor A_2. The communication required to achieve above task is to transmit system A_1 (using log d_{A_1} qubits) from A (Alice) to B (Bob), where B is transformed to B' \tensor B'', with R playing no active role.

This protocol is important as it helps in giving achievable strategies in various other quantum information processing tasks.

Main tool of the proof and hence for the this talk, is decoupling theorem. This theorem is a statement about the extent to which one can eradicate correlation between systems A and R (with the starting state being a density matrix on AR).  We will look at this theorem geometrically.

The necessary terminologies from quantum information theory shall be described along the talk and the only required tool for the talk would be basic linear algebra.