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We examine the possibilities of non-trivial phenomena of time-invariantentanglement and freezing dynamics of entanglement for qutrit-qutrit quantumsystems. We find no evidence for time-invariant entanglement, however, we doobserve that quantum states freeze their entanglement after decaying for sometime. It is interesting that quantum states are changing whereas theirentanglement remains constant. We find that the combined action of decoherencefree subspaces and subspaces where quantum states decay, facilitate thisphenomenon. This study is an extension of similar phenomena observed forqubit-qubit systems, qubit-qutrit, and multipartite quantum systems. We examinenonlocality of a specific family of states and find the certain instances wherethe states still remain entangled, however they can either loose theirnonlocality at a finite time or remain nonlocal for all times.

Freezing dynamics of entanglement and nonlocality for qutrit-qutrit ($3 \otimes 3$) quantum systems