Środowiskowe Seminarium z Informacji i Technologii Kwantowych

The most general quantum object that can be shared between two distant parties is a bipartite quantum channel. While much effort over the last two decades has been devoted to the study of entanglement of bipartite states, very little is known about the entanglement of bipartite channels. In this work, for the first time we rigorously study the entanglement of bipartite channels. We follow a top-down approach, starting from general resource theories of processes, for which we present a new construction of a complete family of monotones, valid in all resource theories where the set of free superchannels is convex. In this setting, we define various general resource-theoretic protocols and resource monotones, which are then applied to the case of entanglement of bipartite channels. We focus in particular on the resource theory of NPT entanglement. Our definition of PPT superchannels allows us to express all resource protocols and monotones in terms of semi-definite programs. Along the way, we generalize the negativity measure to bipartite channels, and show that another monotone, the max-logarithmic negativity, has an operational interpretation as the exact asymptotic entanglement cost of a bipartite channel. Finally, we show that it is not possible to distill entanglement out of bipartite PPT channels under any set of free superchannels that can be used in entanglement theory, leading us in particular to the discovery of bound entangled POVMs.