Operational Classification and Quantification of Multipartite Entangled States

Abstract

We formalize and extend an operational multipartite entanglement measure introduced by T. R. Oliveira, G. Rigolin, and M. C. de Oliveira, Phys. Rev. A 73, 010305(R) (2006), through the generalization of global entanglement (GE) [D. A. Meyer and N. R. Wallach, J. Math. Phys. 43, 4273 (2002)]. Contrarily to GE the main feature of this measure lies in the fact that we study the mean linear entropy of all possible partitions of a multipartite system. This allows the construction of an operational multipartite entanglement measure which is able to distinguish among different multipartite entangled states that GE failed to discriminate. Furthermore, it is also maximum at the critical point of the Ising chain in a transverse magnetic field, being thus able to detect a quantum phase transition.

14 pages, RevTex4, published version

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• Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions
• Constructing N-qubit entanglement monotones from anti-linear operators
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Cited by in corpus (14)

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• Maximally multipartite entangled states
• Multipartite Entanglement Signature of Quantum Phase Transitions
• Hierarchies of Geometric Entanglement
• Multipartite entangled states in particle mixing
• Inductive classification of multipartite entanglement under SLOCC
• Entanglement of two blocks of spins in the critical Ising model
• Symmetry breaking effects upon bipartite and multipartite entanglement in the XY model
• Mutually unbiased bases and generalized Bell states
• Two computable sets of multipartite entanglement measures
• Generalized Quantum Telecloning
• Monogamy Inequality and Residual Entanglement of Three Qubits under Decoherence
• Momentum-space analysis of multipartite entanglement at quantum phase transitions
• Structure of quantum correlations in momentum space and off diagonal long range order in eta pairing and BCS states