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arXiv:1911.09095

Quantum correlations of qubit-qutrit systems under general collective dephasing

Mazhar Ali

Published Nov 20, 2019• 0 citations
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Abstract

Most studies of collective dephasing for bipartite as well as multipartite quantum systems focus on a very specific orientation of magnetic field, that is, z-orientation. However, in practical situations, there are always small fluctuations in stochastic field and it is necessary that more general orientations of fields should be considered. We extend this problem to qubit-qutrit systems and study correlation dynamics for entanglement and local quantum uncertainty for some specific quantum states. We find that certain quantum states exhibit freezing dynamics both for entanglement and local quantum uncertainty. We analyze the asymptotic states and find the conditions for having non-zero entanglement and local quantum uncertainty. Our results are relevant for ion-trap experiments and can be verified with current experimental setups.

DOI
10.48550/arxiv.1911.09095

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Most studies of collective dephasing for bipartite as well as multipartite quantum systems focus on a very specific orientation of magnetic field, that is, z-orientation. However, in practical situations, there are always small fluctuations in stochastic field and it is necessary that more general orientations of fields should be considered. We extend this problem to qubit-qutrit systems and study correlation dynamics for entanglement and local quantum uncertainty for some specific quantum states. We find that certain quantum states exhibit freezing dynamics both for entanglement and local quantum uncertainty. We analyze the asymptotic states and find the conditions for having non-zero entanglement and local quantum uncertainty. Our results are relevant for ion-trap experiments and can be verified with current experimental setups.
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Abstract We investigate a hybrid qubit–qutrit system exposed to both a magnetic field and classical dephasing noise. The quantum system’s characteristics encompass diverse parameters, including spin-exchange interaction, dephasing, and the magnetic field. To incorporate thermal effects, we employ the system’s Hamiltonian to generate an initial qubit–qutrit density matrix within the framework of the Gibbs density operator. Furthermore, we model dephasing effects on the initial thermal state of the system using an Ornstein–Uhlenbeck process. We employ geometric discord, negativity, and entropic coherence functions to depict the quantum correlations across various parameter settings. Our results reveal that initially, quantum correlations attain non-maximal values, with their dynamics intricately reliant on the underlying system parameters. Specifically, when the system is primarily characterized by the magnetic field, we observe heightened levels of quantum correlations. Additionally, temperature-based characterization is found to have the most detrimental effect on the state. Geometric discord is observed to capture a higher degree of quantum correlations, albeit saturating rapidly at zero compared to entanglement and coherence. Finally, we investigated the effects of common environmental coupling and more pronounced non-Markovian dynamics in the system, revealing an enhanced preservation of quantum correlations. These modifications allow for prolonged coherence and entanglement, underscoring the potential of structured environmental interactions to mitigate decoherence effects and sustain quantum correlations over time.
Abstract Recently, local quantum uncertainty (LQU) as a measure of quantum correlations has been proposed by Girolami et al . We here have investigated the LQU dynamics in a pair of qubits system subjected to either local or collective classical phase noises. The explicit analytical expressions of LQU for the two-qubit system of interest initially in a Werner state under these dephasing noises have been derived. We compare the dynamics of LQU with that of entanglement as measured with concurrence. Our results show that LQU always decays asymptotically while the entanglement displays sudden death phenomenon. Besides, there is no simple relation between the LQU and entanglement since LQU may be smaller or larger than entanglement. Finally, we try to protect LQU against the dephasing noise by means of filtering operation.
We study the dynamics of genuine multipartite entanglement for quantum systems upto four qubits interacting with general collective dephasing process. Using a computable entanglement monotone for multipartite systems, we observe the feature of freezing dynamics of genuine entanglement for three and four qubits entangled states. We compare the dynamics with that of random states and find that most states exibit this feature. We then study the effects of collective dephasing on genuine nonlocality and find out that although quantum states remain genuinely entangled yet their genuine nonlocality is lost in a finite time. We show the sensitivity of asymptotic states being genuinely entangled by mixing white noise.
We investigate the mutual information and entanglement of stationary state of two locally driven qubits under the influence of collective dephasing. It is shown that both the mutual information and the entanglement of two qubits in the stationary state exhibit damped oscillation with the scaled action time gammaT\\gamma{T}gammaT of the local external driving field. It means that we can control both the entanglement and total correlation of the stationary state of two qubits by adjusting the action time of the driving field. We also consider the influence of collective dephasing on entanglement of two qutrits and obtain the sufficient condition that the stationary state is entangled.
We examine the possibilities of nontrivial 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 certain 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.