Entanglement of mixed states in systems of n qubits

Mostafa Mansour, Mohammed Daoud A

We derive the entangled thermal mixed states by using the formalism of phase states for a finite-dimensional algebra of a multi-qubit system in contact with an independent thermal environment of absolute temperature [Formula: see text]. Thermal entangled states describing the multi-qubit system in equilibrium with the thermal bath are a special kind of mixed states that exhibit genuine multipartite correlation. We define the unitary phase operators for a multipartite system of non-interacting qubits. Entangled density matrices are derived for qubits interacting via an Hermitian Hamiltonian of Heisenberg type [Formula: see text]. By assuming that the noisy interaction of the entangled qubit ensemble with the bath is governed by a local Hamiltonian [Formula: see text], we show that the entangled phase states can be decohered. When the multi-qubits entangled system reaches the equilibrium with the thermal bath, the decohered mixed states are identified with entangled thermal states. The thermal mixed states for bipartite and multipartite systems are explicitly expressed and their bipartite entanglement properties are investigated.

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Khalid Talbi, Mostafa Mansour

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.

Mikko M. Ervasti

Mostafa Mansour, Saeed Haddadi

In this work, we investigate the bipartite entanglement of decohered mixed states generated from maximally entangled cluster states of [Formula: see text] qubits physical system. We introduce the disconnected cluster states for an ensemble of [Formula: see text] non-interacting qubits and we give the corresponding separable density matrices. The maximally entangled states can be generated from disconnected cluster states, by assuming that the dynamics of the multi-qubit system is governed by a quadratic Hamiltonian of Ising type. When exposed to a local noisy interaction with the environment, the multi-qubit system evolves from its initial pure maximally entangled state to a decohered mixed state. The decohered mixed states generated from bipartite, tripartite and multipartite maximally entangled cluster states are explicitly expressed and their bipartite entanglements are investigated.

Piroska Dömötör, M. G. Benedict