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arXiv:1206.1914

Noisy channel effect on quantum correlations of two relativistic particles

M. Mahdian, T. Makaremi, S. Salimi

Published Jun 9, 2012• 0 citations
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Abstract

We study the quantum correlation dynamics of two relativistic particles which is transmitted through one of the Pauli channels $ σ_{x}, σ_{y},$ and $σ_{z}$. We compare sudden death and robustness of entanglement and geometric discord and quantum discord of two relativistic particles under noisy Pauli channels. we find out geometric discord and quantum discord may be more robust than entanglement against decoherence.

DOI
10.48550/arxiv.1206.1914

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We study the quantum correlation dynamics of two relativistic particles which is transmitted through one of the Pauli channels σx,σy, σ_{x}, σ_{y},σx​,σy​, and σzσ_{z}σz​. We compare sudden death and robustness of entanglement and geometric discord and quantum discord of two relativistic particles under noisy Pauli channels. we find out geometric discord and quantum discord may be more robust than entanglement against decoherence.
We calculate the dissipative dynamics of two-qubit quantum discord under Markovian environments. We analyze various dissipative channels such as dephasing, depolarizing, and generalized amplitude damping, assuming independent perturbation, in which each qubit is coupled to its own channel. Choosing initial conditions that manifest the so-called sudden death of entanglement, we compare the dynamics of entanglement with that of quantum discord. We show that in all cases where entanglement suddenly disappears, quantum discord vanishes only in the asymptotic limit, behaving similarly to individual decoherence of the qubits, even at finite temperatures. Hence, quantum discord is more robust than the entanglement against decoherence so that quantum algorithms based only on quantum discord correlations may be more robust than those based on entanglement.
We calculate the dissipative dynamics of two-qubit quantum discord under Markovian environments. We analyze various dissipative channels such as dephasing, depolarizing, and generalized amplitude damping, assuming independent perturbation, in which each qubit is coupled to its own channel. Choosing initial conditions that manifest the so-called sudden death of entanglement, we compare the dynamics of entanglement with that of quantum discord. We show that in all cases where entanglement suddenly disappears, quantum discord vanishes only in the asymptotic limit, behaving similarly to individual decoherence of the qubits, even at finite temperatures. Hence, quantum discord is more robust than the entanglement against to decoherence so that quantum algorithms based only on quantum discord correlations may be more robust than those based on entanglement.
The dynamics of a geometric measure of the quantum discord (GMQD) under decoherence is investigated. We show that the GMQD of a two-qubit state can be alternatively obtained through the singular values of a 3×43\times43×4 matrix whose elements are the expectation values of Pauli matrices of the two qubits. By using Heisenberg picture, the analytic results of the GMQD is obtained for three typical kinds of the quantum decoherence channels. We compare the dynamics of the GMQD with that of the quantum discord and of entanglement. We show that a sudden change in the decay rate of the GMQD does not always imply that of the quantum discord, and vice versa. We also give a general analysis on the sudden change in behavior and find that at least for the Bell diagonal states, the sudden changes in decay rates of the GMQD and that of the quantum discord occur simultaneously.
We investigate the dynamics of quantum correlations such as entanglement and quantum discord between two noninteracting atoms, each of which is trapped inside one of two coupled cavities. We find that the cavity decay can induce both entanglement and quantum discord between the two atoms when they are initially prepared in doubly excited state. The result shows the sudden death and sudden birth of entanglement and robustness of the quantum discord to sudden death. It is also found that the doubly excited state is responsible for the sudden death of entanglement. Moreover, the sudden death of entanglement can be controlled by the intercavity hopping rate.
By considering a double Jaynes—Cummings model, we investigate the dynamics of quantum correlations, such as the quantum discord and the entanglement, for two atoms in their respective noisy environments, and study the effect of the purity and the cavity temperature on the quantum correlations. The results show that the entanglement suffers sudden death and revival, however the quantum discord can still reveal the quantum correlations between the two atoms in the region where the entanglement is zero. Moreover, when the temperature of each cavity is high the entanglement dies out in a short time, but the quantum discord still survives for quite a long time. It means that the quantum discord is more resistant to environmental disturbance than the entanglement at higher temperatures.
We investigate the dynamics of entanglement and quantum discord of two qubits in liquid state homonuclear NMR. Applying a phenomenological description for NMR under relaxation process, and taking a group of typical parameters of NMR, we show that when a zero initial state $|00> $ experiences a relaxation process, its entanglement disappears completely after a sequence of so-called sudden deaths and revivals, while the quantum discord retains remarkable values after a sequence of oscillations. That is to say, the quantum discord is more robust than entanglement.