In this paper, we first present a simple measure for multiqubit entanglement based on the strategy of bipartite cuts and the measure of negativity. Then, we establish generalized monogamy inequalities and associated partition-dependent residual entanglement (PRE) accounting for arbitrary partitions of a multiqubit system. By virtue of the defined quantities, we investigate the entanglement dynamics of a system of N qubits, either in the Greenberger–Horne–Zeilinger (GHZ)-type state or in the W state, interacting with N independent reservoirs in both Markovian and non-Markovian regimes. We observe entanglement revivals of qubits at instantaneous points of disappearance or after a finite interval of abrupt vanishing due to the memory effect of non-Markovian reservoirs. We also follow the whole entanglement evolution in terms of the PRE to demonstrate the process of transition between the bipartite entanglement of all possible bipartitions and the multipartite entanglement. In particular, we show that the change in time of entanglement formats differs qualitatively for the GHZ-type and W states.
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 behaviour 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 behaviour associated with general initial states.
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.