Decoupling with unitary approximate two-designs

Abstract

Consider a bipartite system, of which one subsystem, A , undergoes a physical evolution separated from the other subsystem, R . One may ask under which conditions this evolution destroys all initial correlations between the subsystems A and R , i.e. decouples the subsystems. A quantitative answer to this question is provided by decoupling theorems , which have been developed recently in the area of quantum information theory. This paper builds on preceding work, which shows that decoupling is achieved if the evolution on A consists of a typical unitary, 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 approximate two-design. A main implication of this result is that decoupling is physical, in the sense that it occurs already for short sequences of random two-body interactions, which can be modeled as efficient circuits. Our decoupling result is independent of the dimension of the R system, which shows that approximate two-designs are appropriate for decoupling even if the dimension of this system is large.