# Qubit-Qutrit ($2 \otimes 3$) quantum systems: An investigation of some quantum correlations under collective dephasing

## TL;DR

This paper investigates qubit-qutrit quantum systems under collective dephasing, revealing the coexistence of time-invariant entanglement and freezing dynamics, which was previously thought to be mutually exclusive.

## Contribution

It demonstrates for the first time that both time-invariant entanglement and freezing dynamics can coexist in qubit-qutrit systems, extending understanding of quantum correlations.

## Key findings

- Both phenomena coexist in qubit-qutrit systems.
- Many states exhibit entanglement freezing after decay.
- Study extends previous work on simpler quantum systems.

## Abstract

We revisit qubit-qutrit quantum systems under collective dephasing and answer some of the questions which have not been asked and addressed so far in the literature. In particular, we examine the possibilities of non-trivial phenomena of {\it time-invariant} entanglement and {\it freezing} dynamics of entanglement for this dimension of Hilbert space. Interestingly, we find that for qubit-qutrit systems both of these peculiar features coexist, that is, we observe not only time-invariant entanglement for certain quantum states but we find also find evidence that many quantum states freeze their entanglement after decaying for some time. To our knowledge, the existance of both these phenomena for one dimension of Hilbert space is not found so far. All previous studies suggest that if there is freezing dynamics of entanglement, then there is no time-invariant entanglement and vice versa. In addition, we study local quantum uncertainity and other correlations for certain families of states and discuss the interesting dynamics. Our study is an extension of similar studies for qubit-qubit systems, qubit-qutrit, and multipartite quantum systems.