Rates of asymptotic entanglement transformations for bipartite mixed states: Maximally entangled states are not special

This work reviews and extends recent results concerning the distribution of entanglement, as well as nonlocality (in terms of inequality violations) in tripartite qubit systems. With recourse to a Monte Carlo generation of pure and mixed states of three-qubits, we explore several features related to the distribution of entanglement (expressed in the form of different measures of multiqubit entanglement based upon bipartitions). Also, special interest is paid to maximally entangled states (such as the GHZ for three-qubits) and W states. This study also sheds some light on the interesting relation existing between some entanglement measures and perfect state discrimination in LOCC measurements relevant to cryptographic protocols. We round off the results by studying the distribution of entanglement between Alice and Bob in a modified teleportation protocol toy model over three-qubit states.

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Bipartite entanglement of decohered mixed states generated from maximally entangled cluster states

Modern Physics Letters A ◽

10.1142/s0217732321500103 ◽

2021 ◽

Vol 36 (03) ◽

pp. 2150010

Author(s):

Mostafa Mansour ◽

Saeed Haddadi

Keyword(s):

Mixed State ◽

Entangled States ◽

Entangled State ◽

Mixed States ◽

Density Matrices ◽

Bipartite Entanglement ◽

Cluster States ◽

Maximally Entangled State ◽

Qubit System ◽

Maximally Entangled States

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.

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Maximally Entangled Mixed States and the Bell Inequality

Zeitschrift für Naturforschung A ◽

10.1515/zna-2001-0123 ◽

2001 ◽

Vol 56 (1-2) ◽

pp. 152-154

Author(s):

W. J. Munro ◽

K. Nemoto

Keyword(s):

Bell Inequality ◽

Maximum Amount ◽

Entangled States ◽

Mixed States ◽

Maximally Entangled States

AbstractRecently a class of maximally entangled states has been proposed that has the maximum amount of entanglement for a given purity. We investigate how much such states violate the conventional Bell inequality and discuss its implication.

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Multipartite entanglement and hyperdeterminants

Quantum Information and Computation ◽

10.26421/qic2.s-4 ◽

2002 ◽

Vol 2 (Special) ◽

pp. 540-555

Author(s):

A. Miyake ◽

M. Wadati

Keyword(s):

Entangled States ◽

Multipartite Entanglement ◽

Maximal Dimension ◽

Ordered Structure ◽

Mixed States ◽

Separable States ◽

Entanglement Measures ◽

Pure States ◽

Maximally Entangled States ◽

Bipartite Case

We classify multipartite entanglement in a unified manner, focusing on a duality between the set of separable states and that of entangled states. Hyperdeterminants, derived from the duality, are natural generalizations of entanglement measures, the concurrence, 3-tangle for 2, 3 qubits respectively. Our approach reveals how inequivalent multipartite entangled classes of pure states constitute a partially ordered structure under local actions, significantly different from a totally ordered one in the bipartite case. Moreover, the generic entangled class of the maximal dimension, given by the nonzero hyperdeterminant, does not include the maximally entangled states in Bell's inequalities in general (e.g., in the \(n \!\geq\! 4\) qubits), contrary to the widely known bipartite or 3-qubit cases. It suggests that not only are they never locally interconvertible with the majority of multipartite entangled states, but they would have no grounds for the canonical \(n\)-partite entangled states. Our classification is also useful for that of mixed states.

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