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International Journal of Quantum Information

TYPICAL BEHAVIOR OF THE GLOBAL ENTANGLEMENT OF AN OPEN MULTIQUBIT SYSTEM IN A NON-MARKOVIAN REGIMEN

A. P. Majtey, Angel Ricardo Plastino

Published Sep 1, 2012• 4 citations
Publisher

Abstract

We investigate the decay of the global entanglement, due to decoherence, of multiqubit systems interacting with a reservoir in a non-Markovian regime. We assume that during the decoherence process each qubit of the system interacts with its own, independent environment. Most previous works on this problem focused on particular initial states or families of initial states amenable of analytical treatment. Here we determine numerically the typical, average behavior of the system corresponding to random initial pure states uniformly distributed (in the whole Hilbert space of n-qubit pure states) according to the Haar measure. We study systems consisting of 3, 4, 5, and 6 qubits. In each case we consider also the entanglement dynamics corresponding to important particular initial states, such as the GHZ states or multiqubit states maximizing the global entanglement, and determine in which cases any of these states is representative of the average behavior associated with general initial states.

DOI
10.1142/s0219749912500633

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We investigate the decay of the global entanglement, due to decoherence, of multiqubit systems interacting with a reservoir in a non-Markovian regime. We assume that during the decoherence process each qubit of the system interacts with its own, independent environment. Most previous works on this problem focused on particular initial states or families of initial states amenable of analytical treatment. Here we determine numerically the typical, average behavior of the system corresponding to random initial pure states uniformly distributed (in the whole Hilbert space of n-qubit pure states) according to the Haar measure. We study systems consisting of 3, 4, 5, and 6 qubits. In each case we consider also the entanglement dynamics corresponding to important particular initial states, such as the GHZ states or multiqubit states maximizing the global entanglement, and determine in which cases any of these states is representative of the average behavior associated with general initial states.
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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.
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We investigate the decay of entanglement, due to decoherence, of multiqubit systems that are initially prepared in highly (in some cases maximally) entangled states. We assume that during the decoherence processes each qubit of the system interacts with its own independent environment. We determine, for systems with a small number of qubits and for various decoherence channels, the initial states exhibiting the most robust entanglement. We also consider a restricted version of this robustness-optimization problem that only involves states equivalent, under local unitary transformations, to the Greenberger-Horne-Zeilinger ∣GHZ⟩|\text{GHZ}⟩∣GHZ⟩ state.
We investigate the patterns in distributions of localizable entanglement over a pair of qubits for random multiqubit pure states. We observe that the mean of localizable entanglement increases gradually with increasing the number of qubits of random pure states while the standard deviation of the distribution decreases. The effects on the distributions, when the random pure multiqubit states are subjected to local as well as global noisy channels, are also investigated. Unlike the noiseless scenario, the average value of the localizable entanglement remains almost constant with the increase in the number of parties for a fixed value of noise parameter. We also find that the maximum strength of noise under which entanglement survives can be independent of the localizable entanglement content of the initial random pure states.
We study the entanglement dynamics of three two-level atoms interacting with a structured reservoir. The atoms are initially prepared in a mixed W state while the reservoir is in the vacuum. We show the dependence of entanglement dynamics on the purity of initial atomic state and on the amount of non-Markovianity. When the initial state of atoms is in a W pure state, the entanglement will decay asymptotically, while it vanishes in a finite time if the initial state is in a mixed W state. In addition, as the memory effect of the environment, entanglement can partially revive after it vanishes, and the revival degree is dependent on the strength of non-Markovian effect. In the end, we consider the entanglement generation and its evolution when the initial state of the atoms system is completely separable.