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International Journal of Quantum Information

RESEARCH ON THE RELATIONSHIP BETWEEN THE SYMMETRICAL COUPLING AND THE NON-MARKOVIAN RELAXATION CHARACTERISTICS

Juju Hu, Y. H. JI, Y. X. YU, Yan Hu

Published Jun 1, 2012• 2 citations
Publisher

Abstract

We make the study of the relationship between symmetrical coupling of coupling qubits and non-Markovian relaxation characteristics by utilizing concurrence. The results show that the relaxation characteristics of quantum system strongly depend on the coupling way between qubits and environment and the decoherence-free subspace may form under certain conditions. We find that when the system is initially at [Formula: see text] state or the mixed state generated by this state, we can make the quantum system always at the entangled state without entanglement sudden death (ESD) phenomenon by regulating the coupling between qubits and environment at complete anti-symmetric state. In contrast, when the system is initially at [Formula: see text] state or the mixed state generated by this state, then we must regulate the coupling way between qubits and environment at complete symmetric state to make the quantum system maintain at the entanglement state.

DOI
10.1142/s0219749912500438

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We make the study of the relationship between symmetrical coupling of coupling qubits and non-Markovian relaxation characteristics by utilizing concurrence. The results show that the relaxation characteristics of quantum system strongly depend on the coupling way between qubits and environment and the decoherence-free subspace may form under certain conditions. We find that when the system is initially at [Formula: see text] state or the mixed state generated by this state, we can make the quantum system always at the entangled state without entanglement sudden death (ESD) phenomenon by regulating the coupling between qubits and environment at complete anti-symmetric state. In contrast, when the system is initially at [Formula: see text] state or the mixed state generated by this state, then we must regulate the coupling way between qubits and environment at complete symmetric state to make the quantum system maintain at the entanglement state.
The entanglement evolution of the coupled qubits interacting with a non-Markov environment is investigated in terms of concurrence. The results show that the entanglement of the quantum systems depends not only on the initial state of the system but also on the coupling between the qubit and the environment. For the initial state , the coupled qubits will always been in the maximum entangled state under an asymmetric coupling. For the initial state , in contrast, the entangling degree of the coupled qubits is always equal to unity and does not depend on the evolving time under the symmetric coupling. We find that the stronger the interaction between the qubits is, the better the struggle against the entanglement sudden death is.
The evolution of entangled decoherence of coupling superconducting qubits in non-Markovian environment is investigated in detail using concurrence function.The results show that,for coupling superconducting qubit under different entangled initial states,because of the role of memory feedback due to environmental effect,the entanglement of coupling superconducting qubits under a thermal bath always tends to zero monotonically.Further results also showed that,the sudden death of entanglement will soon occur in non-Markovian process,stronger the dissipation,faster the death of entanglement.But in Markovian process,it tends to death of entanglement slowly.
We analyze the dynamics of the entanglement in two independent non-Markovian channels. In particular, we focus on the entanglement dynamics as a function of the initial states and the channel parameters like the temperature and the ratio rrr between ω0ω_0ω0​ the characteristic frequency of the quantum system of interest, and ωcω_cωc​ the cut-off frequency of Ohmic reservoir. We give a stationary analysis of the concurrence and find that the dynamic of non-markovian entanglement concurrence Cρ(t)\mathcal{C}_ρ(t)Cρ​(t) at temperature kBT=0k_BT=0kB​T=0 is different from the kBT>0k_BT>0kB​T>0 case. We find that "entanglement sudden death" (ESD) depends on the initial state when kBT=0k_BT=0kB​T=0, otherwise the concurrence always disappear at finite time when kBT>0k_BT>0kB​T>0, which means that ESD must happen. The main result of this paper is that the non-Markovian entanglement dynamic is fundamentally different from the Markovian one. In the Markovian channel, entanglement decays exponentially and vanishes only asymptotically, but in the non-Markovian channel the concurrence Cρ(t)\mathcal{C}_ρ(t)Cρ​(t) oscillates, especially in the high temperature case. Then an open-loop controller adjusted by the temperature is proposed to control the entanglement and prolong the ESD time.
environment on the entanglement dynamics in non-Markov process. Our results show that the entanglement degree is strongly related with the initial quantum state and the coupling between the qubits and the environment. The interaction between the qubits and the environment suppresses the decay of the entanglement. The sudden death of entanglement (ESD) can be prevented only by using and controlling targeted the interaction model between the different qubits and the environment. We also find the dissipation phenomenon always exists when the qubits system is initially in the maximally entangled mixed states.
We investigate the entanglement dynamics of the bipartite quantum system between two qubits with the dissipative environment. We begin with the standard Markovian master equation in the Lindblad form and the initial state which is prepared in the extended Werner-like state: ρ Φ AB (0). We examine the conditions for entanglement sudden death (ESD) and calculate the corresponding ESD time by the Wootters concurrence. We observe that ESD is determined by the parameters such as the mean occupation number of the environment N , amount of initial entanglement α and the purity r . For N = 0, we get the analytical expressions of both ESD condition and ESD time. For N > 0 we give a theoretical analysis that ESD always occurs, and simulate the concurrence as a function of γ 0 t and one of the parameters N , α and r .