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Decoherence of maximally mixed multi-qubit cluster states

Khalid Talbi, Mostafa Mansour

Published Jun 26, 2019• 0 citations
OpenAlex

Abstract

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.

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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.
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.
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.
This paper concerns the construction of k-uniform maximally mixed multipartite states by using the formalism of phase states for finite dimensional systems (qudits). The k-uniform states are a special kind of entangled (n)-qudits states, such that after tracing out arbitrary (n[Formula: see text]k) subsystems, the remaining (k) subsystems are maximally mixed. We recall some basic elements about unitary phase operators of a multi-qudit system and we give the corresponding separable density matrices. Evolved density matrices arise when qudits of the multipartite system are allowed to interact via an Hamiltonian of Heisenberg type. The expressions of maximally mixed states are explicitly derived from multipartite evolved phase states and their properties are discussed.
We derive absolutely maximally entangled (AME) states from phase states for a multi-qudit system whose dynamics is governed by a two-qudit interaction Hamiltonian of Heisenberg type. AME states are characterized by being maximally entangled for all bipartitions of the multi-qudit system and present absolute multipartite entanglement. The key ingredient of this approach is the theory of phase states for finite-dimensional systems (qudits). We define further the unitary phase operators of [Formula: see text]-qudit systems and we give next the corresponding separable phase states. Using a qudit–qudit Hamiltonian acting as entangling operator on separable phase states, we generate entangled phase states. Finally, from the labeled entangled phase states, we derive the absolutely maximally entangled states.
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.
Self-interactions and interaction with the environment inevitably push quantum systems towards highly mixed states, which is the definition of decoherence. However, if decoherence is completely suppressed, then any quantum system evolves unitarily through pure states towards maximally entangled configurations. We argue that these maximally entangled states of the systems fall into the well-defined classes that can be uniquely described by the values of certain entanglement invariants. After discussing these ideas, we present examples of maximally entangled states for a number of generic systems, construct compact states in the most entangled classes for tripartite systems, and suggest how they may be constructed for other [Formula: see text]-partite systems. We study random walks through the space of entanglement classes to see how unitary evolution along paths to the maximally entangled states, i.e. entanglement growth, works in practice.