Catalytic Decoupling of Quantum Information

The decoupling technique is a fundamental tool in quantum information theory with applications ranging from thermodynamics to many-body physics and black hole radiation whereby a quantum system is decoupled from another one by discarding an appropriately chosen part of it. Here, we introduce catalytic decoupling, i.e., decoupling with the help of an independent system. Thereby, we remove a restriction on the standard decoupling notion and present a tight characterization in terms of the max-mutual information. The novel notion unifies various tasks and leads to a resource theory of decoupling.

Figure 1

Schematic representation of (a) standard and (b) catalytic decoupling: tracing out a system $A_2$ leaves system $A_1$ decoupled from $E$. While there is no ancilla for standard decoupling as in (a), catalytic decoupling as in (b) allows us to make use of an additional, already decoupled system $A^{\prime }$. The basic question is how large we have to choose the system $A_2$ such that system $A_1$ is decoupled from $E$.