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Open Systems & Information Dynamics

Evolution of Genuine Multipartite Entanglement of Specific and Random States Under non-Markovian Noise

Mazhar Ali

Published Dec 1, 2014• 6 citations
Publisher

Abstract

We study the dynamics of genuine multipartite entanglement under non-Markovian noise. Using a computable entanglement monotone for multipartite systems, we investigate a system of three qubits each of which is individually exposed to classical Ornstein–Uhlenbeck noise. We found that the W state mixed with the maximally mixed state is the most fragile state, whereas a similar mixture of GHZ state exhibits robust behaviour. We compare dynamics of these states with dynamics of similar mixtures of random states and weighted graph states. We also discuss the limiting cases.

DOI
10.1142/s1230161214500085

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Characterizing large noisy multiparty quantum states using genuine multipartite entanglement is a challenging task. In this paper, we calculate lower bounds of genuine multipartite entanglement localized over a chosen multiparty subsystem of multiqubit stabilizer states in the noiseless and noisy scenarios. In the absence of noise, adopting a graph-based technique, we perform the calculation for arbitrary graph states as representatives of the stabilizer states and show that the graph operations required for the calculation have a polynomial scaling with the system size. As demonstrations, we compute the localized genuine multipartite entanglement over subsystems of large graphs having linear, ladder, and square structures. We also extend the calculation for graph states subjected to single-qubit Markovian or non-Markovian Pauli noise on all qubits and demonstrate, for a specific lower bound of the localizable genuine multipartite entanglement corresponding to a specific Pauli measurement setup, the existence of a critical noise strength beyond which all of the postmeasured states are biseparable. The calculation is also useful for arbitrary large stabilizer states under noise due to the local unitary connection between stabilizer states and graph states. We demonstrate this by considering a toric code defined on a square lattice and computing a lower bound of localizable genuine multipartite entanglement over a nontrivial loop of the code. Similar to the graph states, we show the existence of the critical noise strength in this case also and discuss its interesting features.
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