Freezing dynamics of entanglement and nonlocality for qutrit-qutrit (3 ⊗ 3) quantum systems

Abstract

We examine the possibilities of non-trivial phenomena of time-invariant entanglement and freezing dynamics of entanglement for qutrit-qutrit quantum systems. We find no evidence for time-invariant entanglement, however, we do observe that quantum states freeze their entanglement after decaying for some time. It is interesting that quantum states are changing whereas their entanglement remains constant. We find that the combined action of decoherence free subspaces and subspaces where quantum states decay, facilitate this phenomenon. This study is an extension of similar phenomena observed for qubit-qubit systems, qubit-qutrit, and multipartite quantum systems. We examine nonlocality of a specific family of states and find the certain instances where the states still remain entangled, however they can either loose their nonlocality at a finite time or remain nonlocal for all times.

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

“…On the other hand, for four qubits, we found no evidence for freezing dynamics of entanglement but we do found time-invariant entanglement [33]. More recently, we examined qutrit-qutrit quantum systems where we found freezing dynamics of entanglement but no time-invariant entanglement [34]. There is no concrete mathematical arguments for mutual exclusiveness of these features for any specific Hilbert space.…”

“…More recently, we have explored the possibility of either time-invariant entanglement or freezing dynamics for qutrit-qutrit (3 ⊗ 3) systems [34]. We found no evidence for time-invariant entanglement, however we observed the exclusive evidence for freezing dynamics of entanglement [34]. We have noticed that in all previous studies on time-invariant entanglement and freezing dynamics for a given Hilbert space, there is either time-invariant entanglement or freezing dynamics behavior.…”

“…Recently, we have explored freezing dynamics for various genuine multipartite specific states of three and four qubits, including random states and found evidence for it [32]. More recently, we have explored the possibility of either time-invariant entanglement or freezing dynamics for qutrit-qutrit (3 ⊗ 3) systems [34]. We found no evidence for time-invariant entanglement, however we observed the exclusive evidence for freezing dynamics of entanglement [34].…”