Trace-distance correlations for X states and emergence of the pointer basis in Markovian and non-Markovian regimes

TL;DR

This paper derives analytical formulas for trace-norm geometric correlations in two-qubit X states and demonstrates how these correlations reveal the emergence of the pointer basis during decoherence in both Markovian and non-Markovian regimes, highlighting non-Markovian effects like delayed information retrieval.

Contribution

It provides the first analytical expressions for trace-norm geometric correlations in X states and links these correlations to the emergence of the pointer basis under decoherence.

Findings

Geometric classical correlations characterize pointer basis emergence.

Non-Markovian effects cause a time delay in information retrieval.

A nonzero measure set of initial states show sudden correlation transitions.

Abstract

We provide analytical expressions for classical and total trace-norm (Schatten 1-norm) geometric correlations in the case of two-qubit X states. As an application, we consider the open-system dynamical behavior of such correlations under phase and generalized amplitude damping evolutions. Then, we show that geometric classical correlations can characterize the emergence of the pointer basis of an apparatus subject to decoherence in either Markovian or non-Markovian regimes. In particular, as a non-Markovian effect, we obtain a time delay for the information to be retrieved from the apparatus by a classical observer. Moreover, we show that the set of initial X states exhibiting sudden transitions in the geometric classical correlation has nonzero measure.