Decoupling with unitary approximate two-designs

TL;DR

This paper proves a generalized decoupling theorem using approximate two-designs, showing that decoupling occurs efficiently with short sequences of random two-body interactions, regardless of the size of the environment system.

Contribution

It extends decoupling theorems to approximate two-designs, demonstrating their physical relevance and efficiency in quantum information processes.

Findings

Decoupling occurs with short sequences of random two-body interactions.

Approximate two-designs are effective for decoupling regardless of environment size.

Decoupling is achievable with efficient quantum circuits.

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 2-designs are appropriate for decoupling even if the dimension of this system is large.