Dissipative and Non-dissipative Single-Qubit Channels: Dynamics and Geometry

TL;DR

This paper analyzes single-qubit quantum channels, focusing on amplitude damping and depolarizing types, exploring their geometry, decoherence, and effects of environmental factors like temperature and squeezing.

Contribution

It provides a canonical Kraus representation for amplitude damping channels using Choi isomorphism and characterizes their geometric and decoherence properties.

Findings

Amplitude damping channels do not form a convex set.

The rank of amplitude damping channels is 2 or 4.

Environmental squeezing can enhance state distinguishability despite decoherence.

Abstract

Single-qubit channels are studied under two broad classes: amplitude damping channels and generalized depolarizing channels. A canonical derivation of the Kraus representation of the former, via the Choi isomorphism is presented for the general case of a system's interaction with a squeezed thermal bath. This isomorphism is also used to characterize the difference in the geometry and rank of these channel classes. Under the isomorphism, the degree of decoherence is quantified according to the mixedness or separability of the Choi matrix. Whereas the latter channels form a 3-simplex, the former channels do not form a convex set as seen from an ab initio perspective. Further, where the rank of generalized depolarizing channels can be any positive integer upto 4, that of amplitude damping ones is either 2 or 4. Various channel performance parameters are used to bring out the different influences of temperature and squeezing in dissipative channels. In particular, a noise range is identified where the distinguishability of states improves inspite of increasing decoherence due to environmental squeezing.