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arXiv:1004.3748 · Physical Review A

Entanglement dynamics in three-qubit X states

Yaakov S. Weinstein

Published Sep 27, 2010• 46 citations
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Abstract

I explore the entanglement dynamics of a three-qubit system in an initial $X$ state undergoing decoherence including the possible exhibition of entanglement sudden death. To quantify entanglement I utilize negativity measures and make use of appropriate entanglement witnesses. The negativity results are then extended to $X$ states with an arbitraty number of qubits. I also demonstrate nonstandard behavior of the tripartite negativity entanglement metric: its sudden appearance after some amount of decoherence, followed quickly by its disappearance. Finally, I solve for a lower bound on the three-qubit $X$-state concurrence, demonstrate when this bound goes to $0$, and outline simplifcations for the calculation of higher-order $X$-state concurrences.

DOI
10.1103/physreva.82.032326

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I explore entanglement dynamics in a three qubit system comparing the ability of entanglement witnesses to detect tripartite entanglement to the phenomenon of entanglement sudden death (ESD). Using a system subject to dephasing I invoke entanglement witnesses to detect tripartite Greenberger-Horne-Zeilinger (GHZ)-type and WWW-type entanglement and compare the evolution of their detection capabilities with the evolution of the negativity, bipartite concurrence, and tripartite negativity. Interestingly, I find a state in which there is no concurrence or tripartite negativity but there is entanglement. Finally, I utilize a three qubit quantum error correction code to address how ESD affects the abilities of quantum error correction.
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 .
In this work, we consider non-interacting atomic two level and three level (qubit-qutrit) systems interacting with a common environment in vacuum state. The interaction with the environment leads to the decoherece of the system due to spontaneous emission of atomic excited states which results in the decay of entanglement and other correlations of the qubit-qutrit system. We study the dynamics of entanglement for different initial class of states and negativity is used as a measure to quantify the degree of entanglement of qubit-qutrit system, the three level systems are considered in V configuration. We construct a class of rank dependant mixed boundary qubit-qutrit states as initial states. We observe entanglement sudden death for higher rank mixed boundary qubit-qutrit states.
I explore the entanglement dynamics of multiqubit systems suitable for use as quantum memories: decoherence free subspaces and noiseless subsystems. The aim of this exploration is to determine how a complete loss of entanglement affects the ability of these error-avoidance techniques to protect quantum information. I utilize negativity and concurrence as entanglement measures and find no correlation between complete system loss of entanglement and the fidelity of the stored quantum information. These results complement previous results in which quantum protocols not explicitly based on entanglement exhibit little correlation between entanglement sudden death and the accuracy of the given protocol.
Using simple models of radiation-matter interaction we study the reduced dynamics of a quantum central system formed by two qubits under the spectator configuration. Purity and concurrence as measures of decoherence and entanglement are evaluated in analytical form. Interestingly in these systems, entanglement sudden death is found despite having less complex dynamics than models used in previous studies. Furthermore, we have analysed the associated local quantum operations generated by the dynamics and how their action on an initial Bell state is characterized in the concurrence-purity diagram.
When an initially entangled pair of qubits undergoes local decoherence processes, there are a number of ways in which the original entanglement can spread throughout the multipartite system consisting of the two qubits and their environments. Here, we report theoretical and experimental results regarding the dynamics of the distribution of entanglement in this system. The experiment employs an all optical setup in which the qubits are encoded in the polarization degrees of freedom of two photons, and each local decoherence channel is implemented with an interferometer that couples the polarization to the path of each photon, which acts as an environment. We monitor the dynamics and distribution of entanglement and observe the transition from bipartite to multipartite entanglement and back, and show how these transitions are intimately related to the sudden death and sudden birth of entanglement. The multipartite entanglement is further analyzed in terms of three- and four-partite entanglement contributions, and genuine four-qubit entanglement is observed at some points of the evolution.