Qubit-Qutrit (2 ⊗ 3) Quantum Systems: an Investigation of Some Quantum Correlations Under Collective Dephasing

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 time-invariant entanglement and 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 also find evidence that many quantum states freeze their entanglement after decaying for some time. To our knowledge, the existence of both these phenomena for a 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 uncertainty and other correlations for certain families of states and discuss the interesting dynamics. Our study is an extension of similar studies for qubit-qubit, qubit-qutrit, and multipartite quantum systems.