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IEEE International Conference on Information and Automation (ICIA)

Optimized control of geometric quantum discord

Juju Hu, Qiang Ke

Published Aug 1, 2015• 0 citations
Publisher

Abstract

We investigate the geometric quantum discord of coupling superconducting qubits in Fock state. In the non-Markovian noisy channel, the geometric quantum discord exhibits typical sudden change. The quantum correlation effect between qubits can be enhanced greatly and the initial disappearance time of entanglement can be delayed under certain circumstance through linearly modulating the coupling coefficient between qubits by a proper control function.

DOI
10.1109/icinfa.2015.7279684

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We investigate the geometric quantum discord of coupling superconducting qubits in Fock state. In the non-Markovian noisy channel, the geometric quantum discord exhibits typical sudden change. The quantum correlation effect between qubits can be enhanced greatly and the initial disappearance time of entanglement can be delayed under certain circumstance through linearly modulating the coupling coefficient between qubits by a proper control function.
A system consists of two charged qubits are initially prepared in a maximum entangled Bell state and having no mutual interaction, where each qubit interacts independently with a superconducting transmission line resonator. An analytical solution of the time evolution of the final state of the system with the effect of a phase decoherence is found. In previous works, quantum correlations are only investigated in X-state for the models which are as our model. In this work, the analytical formulas of the geometric quantum discord (GQD) and measurement-induced non-locality (MIN) are introduced for a general state of two-qubit (non-X-state). Quantum correlations are studied via GQD and MIN with quantum entanglement (QE). It is found that a sudden disappearance only occurs for QE, while MIN and GQD still exist. Due to the increase in the amplitude of the coherent states, the intervals of the sudden disappearance of QE increase and MIN and GQD decrease. It is interesting to note that initial correlations can be lost and they reach their stationary correlations with the increase in the intrinsic decoherence. The stationary correlation of MIN can be destroyed, it reach zero value, when both the decoherence effect and detuning are present simultaneously. By starting with different types of Bell-like states, the stationary correlations as well as the time intervals of sudden disappearance have notable changes. It is possible to control the quantum correlations with certain parameter sets.
Abstract We investigate the influence of a time-dependent electromagnetic field (TDEF) on the double sudden change of the 1-norm geometric quantum discord (GQD) and sudden change of quantum coherence for superconducting circuit systems under spontaneous emission, where two superconducting qubits are each coupled to their own LC circuit or uniformly coupled to a common LC circuit, respectively. It is shown that the double sudden change of the GQD can be controlled, and the frozen time during which the GQD keeps nearly constant can be lengthened by applying the TDEF. Furthermore, we also find that the TDEF can delay the ‘critical point’ of sudden change for quantum coherence and slow down the decay of quantum coherence. Finally, we explore how the TDEF affects the superconducting circuits system’s information flow by using trace distance and the optimal control scheme is sought by comparing the two coupled modes.
We study the non-Markovian effect on the dynamics of the quantum discord by exactly solving a model consisting of two independent qubits subject to two zero-temperature non-Markovian reservoirs, respectively. Considering the two qubits initially prepared in Bell-like or extended Werner-like states, we show that there is no occurrence of the sudden death, but only instantaneous disappearance of the quantum discord at some time points, in comparison to the entanglement sudden death in the same range of the parameters of interest. This implies that the quantum discord is more useful than the entanglement to describe the quantum correlation involved in quantum systems.
Quantum entanglement plays a key role in quantum information and quantum computation and thus attracts much attention in many branches of physics both in theory and in experiment. But recent studies revealed that some separable states (non-entangled state) may speed up certain tasks over their classical counterparts and may also possess certain kinds of quantum correlations. For example, geometric quantum discord, which is a more general quantum correlation measure than entanglement, can be nonzero for some separable states. From a practical point of view, it is proposed that the geometric quantum discord be responsible for the power of many quantum information processing tasks. In order to capture such correlations, Ollivier and Zurek introduced quantum discord, which measures the discrepancy between two natural yet different quantum analogues of two classically equivalent expressions of mutual information. However, the calculation of quantum discord is based on numerical maximization procedure, and there are few analytical expressions even for a two-qubit state. In order to obtain the analytical results of quantum discord, a geometric measure of quantum discord which measures the quantum correlations through the minimum Hilbert-Schmidt distance between the given state and zero discord state is introduced. Geometric quantum discord is defined as an effective measure of quantum correlation, and the geometric quantum discord through the minimal distance between the quantum state and the set of zero-discord states in a bipartite quantum system can be worked out. In this paper, by using the geometric quantum discord measurement method, the geometric quantum discord in Tavis-Cummings model is investigated, and the influences of the initial state purity, entanglement degree, dipole-dipole coupling intensity between two atoms, and field in the Fock state on the evolution characteristic of geometric quantum discord are analyzed. The results show that the geometric quantum discord appears periodically. It initially decreases to a minimum value, and then turns out to be increased for different initial states. The rigorous analysis and numerical results reveal that when we take a suitable initial state, the geometric quantum discord of two atoms can be kept in correlation. When the atoms are in the different initial states, the quantum properties of the system are significant. The photon number of the field can lead the quantum discord to be weakened. Geometric quantum discord can be increased by increasing the cavity photon number and the dipole-dipole coupling intensity. Geometric quantum discord can be enhanced obviously by increasing the strength of the dipole-dipole coupling interaction. The conclusions may conduce to the understanding of quantum correlation for the other systems from the view of geometric quantum discord.
Abstract We investigate the time evolution of quantum correlations of a hybrid qubit-qutrit system under the classical Ornstein-Uhlenbeck (OU) noise. Here we consider two different one-parameter families of qubit-qutrit states which independently interact with the non-Markovian reservoirs. A comparison with the Markovian dynamics reveals that for the same set of initial condition parameters, the non-Markovian behavior of the environment plays an important role in the enhancement of the survival time of quantum correlations. In addition, it is observed that the non-Markovian strength ( γ / Γ ) has a positive impact on the correlations time. For the initial separable states it is found that there is a finite time interval in which the geometric quantum discord is frozen despite the presence of a noisy environment and that interval can be further prolonged by using the non-Markovian property. Moreover, its decay can be significantly delayed .
We examined decay dynamics of various geometric quantum discords (GQDs) for two interacting qubits described by the Heisenberg XY model and further coupled independently to their respective thermal reservoirs. Compared to the case of noninteracting qubits, our results showed that decay rates of the GQDs can be retarded apparently by properly choosing system parameters of the interaction term. In the long-time limit, the asymptotic values of the GQDs are enhanced evidently by tuning anisotropy of the model and strength of the transverse magnetic field. We further illuminated the relations between different GQDs on characterizing quantum correlations, and observed multiple sudden change behaviors of their dynamics.