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arXiv:2109.11548 · Quantum Information Processing

Multipartite mixed maximally entangled states: mixed states with entanglement 1

Samuel R. Hedemann

Published Mar 31, 2022• 1 citation
arXivHTMLPDF
DOI
10.1007/s11128-022-03458-0

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The maximally entangled state can be in a mixed state as well as the well-known pure state. Taking the negativity as a measure of entanglement, we study the entanglement dynamics of bipartite, mixed maximally entangled states (MMESs) in multipartite cavity-reservoir systems. It is found that the MMES can exhibit the phenomenon of entanglement sudden death, which is quite different from the asymptotic decay of the pure-Bell-state case. We also find that maximal entanglement cannot guarantee maximal nonlocality, and the MMES does not correspond to the state with maximal measurement-induced nonlocality (MIN). In fact, the value and dynamic behavior of the MIN for the MMESs are dependent on the mixed-state probability. In addition, we investigate the distributions of negativity and the MIN in a multipartite system, where the two types of correlations have different monogamous properties.
The maximally entangled state can be the mixed state form beside the well-known pure state case. As quantified by the negativity, we study the entanglement dynamics of bipartite mixed maximally entangled state (MMES) in multipartite cavity-reservoir systems. It is found that the MMES can exhibit the phenomenon of entanglement sudden death, which is quite different to the asymptotic decay of pure state case. Moreover, we find that the maximal entanglement cannot guarantee the maximal nonlocality. The measurement-induced nonlocality (MIN) of MMES is not always the maximal, and its value and dynamical behavior are dependent on the mixed probability. In addition, we investigate the distributions of negativity and MIN in the multipartite system, where the two types of correlations have different monogamous properties in the dynamical procedure.
We investigate the decoherence of maximally mixed multi-partite cluster states of a physical system of n qubits. We introduce the disconnected cluster states for an ensemble of non interacting qubits and we give the corresponding separable density matrices. The maximally entangled cluster states can be generated from disconnected cluster states, by applying the entanglig operators between the pair of qubits. When exposed to a local noisy interaction with the environment, the multi-qubit system evolves from its initial pure maximally entangled cluster state to a decohered mixed state. The deco-hered mixed states for multipartite systems are explicitly expressed and their bipartite entanglement is characterized by using the genuine multipartite neg-ativity as a quantifier of entanglement. Conclusion Entangled cluster states are obtained by a dynamical evolution of multi-qubit system by using an Hamiltonian of Ising type. Cluster states are of great interest in quantum computing and are suitable in various tasks of quantum computation. Decohered mixed states are derived via a local noisy evolution of the entangled multi-qubit system in contact with environment. More precisely , under the influence of the de-coherence, the multi-qubit system loses entanglement and evolves from it's initial maximally entangled cluster state to a decohered mixed state. More precisely we have given explicit expressions of decohered mixed states derived from n-qubit entangled cluster states. The separability for decohered mixed states is addressed with the concept of the genuine multipartite nega-tivity.