Decoupling with unitary almost two-designs

Abstract

Consider a bipartite system, of which one subsystem, A, undergoes a physical evolution separated from the other subsystem, R. We are interested in conditions under which this evolution destroys all initial correlations between the subsystems A and R, i.e. decouples the subsystems. Quantitatively this is done in terms of decoupling theorems. Such theorems have proven useful in various applications in the area of quantum information theory. This paper builds on preceding work, which shows that decoupling can be achieved by applying a typical unitary on A chosen with respect to the Haar measure followed by a process that adds sufficient decoherence. Here, we prove a generalized decoupling theorem for the case where the unitary is chosen from an almost two-design. A main implication of this result is that decoupling is physical, in the sense that it can be achieved by short sequences of random two-body interactions, which can be modeled as efficient circuits. We discuss applications of this result.