Geometric Characterization of True Quantum Decoherence

TL;DR

This paper introduces a geometric measure to distinguish true quantum decoherence channels from classical fluctuation-induced ones, revealing the structure of quantum phase-damping channels and their relation to SIC-POVMs.

Contribution

It develops a simple geometric measure to characterize true quantum decoherence channels and relates maximum quantumness to SIC-POVMs, advancing understanding of quantum noise.

Findings

The measure can be directly assessed from the channel's matrix representation.

True quantum channels are characterized by their distance from the convex set of RU channels.

Maximum quantumness is linked to a symmetric SIC-POVM on the environment.

Abstract

Surprisingly often decoherence is due to classical fluctuations of ambient fields and may thus be described in terms of random unitary (RU) dynamics. However, there are decoherence channels where such a representation cannot exist. Based on a simple and intuitive geometric measure for the distance of an extremal channel to the convex set of RU channels we are able to characterize the set of true quantum phase-damping channels. Remarkably, using the Caley-Menger determinant, our measure may be assessed directly from the matrix representation of the channel. We find that the channel of maximum quantumness is closely related to a symmetric, informationally-complete positive operator-valued measure (SIC-POVM) on the environment. Our findings are in line with numerical results based on the entanglement of assistance.