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arXiv:0711.4799 · Physical Review A

Entanglement dynamics of two independent qubits in environments with and without memory

Bruno Bellomo, Rosario Lo Franco, Giuseppe Compagno

Published Mar 26, 2008• 286 citations
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Abstract

Here is analyzed the dynamics of two-qubit entanglement, when the two qubits are initially in a mixed extended Werner-like state and each of them is in a zero temperature non-Markovian environment. The dependence of entanglement dynamics on the purity and degree of entanglement of the initial states and on the amount of non-Markovianity is also given. This extends the previous work about non-Markovian effects on the two-qubit entanglement dynamics for initial Bell-like states [Bellomo et al., Phys. Rev. Lett. 99, 160502 (2007)]. The effect on the two-qubit entanglement dynamics of nonzero temperature in Markovian environments is finally studied.

DOI
10.1103/physreva.77.032342

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Here is analyzed the dynamics of two-qubit entanglement, when the two qubits are initially in a mixed extended Werner-like state and each of them is in a zero temperature non-Markovian environment. The dependence of entanglement dynamics on the purity and degree of entanglement of the initial states and on the amount of non-Markovianity is also given. This extends the previous work about non-Markovian effects on the two-qubit entanglement dynamics for initial Bell-like states [Bellomo et al., Phys. Rev. Lett. 99, 160502 (2007)]. The effect on the two-qubit entanglement dynamics of nonzero temperature in Markovian environments is finally studied.
We investigate the sudden birth and sudden death of entanglement of two qubits interacting with un-correlated structured reservoirs. The system is initially prepared in two-qubit extended Werner-like state. We work out the dependence of the entanglement dynamics on both non-Markovian environments and the purity of initial state, and show that non-Markovian environments and the purity can control the time of the two-qubit entanglement sudden death and the reservoirs' entanglement sudden birth. Furthermore, under the conditions of different purity and initial entanglement, the revival of qubits' entanglement can manifest before, simultaneously or even after the disentanglement of their corresponding reservoirs.
We explore various aspects of the quantum entanglement dynamics of systems of two, three and four qubits interacting with an environment at zero temperature in a non-Markovian regime, as described by the paradigmatic model recently studied by Bellomo et al (2007 Phys. Rev. Lett. 99 160502). We consider important families of initial states for the alluded systems. The average, typical entanglement evolution associated with each of these families is determined, and its relation with the evolution of the global degree of mixedness of the multi-qubit system is explored. For three and four qubits we consider the family of initial states equivalent under local unitary transformations to the |GHZ⟩ and | W ⟩ states, and compare their average behavior with the average behavior exhibited by initial maximally entangled two-qubit states. Furthermore, in the case of two qubits, the evolution of other manifestations of entanglement, related to measurable quantities, is also investigated. In particular, we consider the Mintert–Buchleitner concurrence lower bound and an entanglement indicator based upon the violation of local uncertainty relations.
Two noninteracting qubits, initially prepared in an entangled state, are coupled to their own independent environments and evolve under their influence. The reduced non-Markovian dynamics of two qubits is exact for arbitrary model parameters. Necessary and sufficient conditions for nonvanishing entanglement are formulated for both zero and nonzero temperatures and arbitrary time. It is shown that (i) entanglement dynamics can effectively be controlled by a finite quantum system coupled to one of the qubits and (ii) dynamical symmetry of the controlling quantum system can influence significantly entanglement of the qubits and results in its nonmonotonic decay.
We provide an analytical investigation of the pairwise entanglement dynamics for a system, consisting of an arbitrary number of qubits dissipating into a common and non-Markovian environment for both weak- and strong-coupling regimes. In the latter case, a revival of pairwise entanglement due to the memory depth of the environment is observed. The leakage of photons into a continuum state is assumed to be the source of dissipation. We show that for an initially Werner state, the environment washes out the pairwise entanglement, but a series of nonselective measurements can protect the relevant entanglement. On the other hand, by limiting the number of qubits initially in the superposition of single excitation, a stationary entanglement can be created between qubits initially in the excited and ground states. Finally, we determine the stationary distribution of the entanglement versus the total number of qubits in the system.