Geometric multipartite entanglement measures

Abstract Genuine entanglement is the strongest form of multipartite entanglement. Genuinely entangled pure states contain entanglement in every bipartition and as such can be regarded as a valuable resource in the protocols of quantum information processing. A recent direction of research is the construction of genuinely entangled subspaces — the class of subspaces consisting entirely of genuinely entangled pure states. In this paper we present methods of construction of such subspaces including those of maximal possible dimension. The approach is based on the composition of bipartite entangled subspaces and quantum channels of certain types. The examples include maximal subspaces for systems of three qubits, four qubits, three qutrits. We also provide lower bounds on two entanglement measures for mixed states, the concurrence and the convex-roof extended negativity, which are directly connected with the projection on genuinely entangled subspaces.

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Additive multipartite entanglement measures

International Conference on Quantum Information ◽

10.1364/icqi.2007.jwc40 ◽

2007 ◽

Author(s):

Gerardo A. Paz-Silva ◽

John H. Reina

Keyword(s):

Multipartite Entanglement ◽

Entanglement Measures

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A Brief Overview of Bipartite and Multipartite Entanglement Measures

International Journal of Theoretical Physics ◽

10.1007/s10773-018-3903-3 ◽

2018 ◽

Vol 57 (12) ◽

pp. 3912-3916 ◽

Cited By ~ 11

Author(s):

Saeed Haddadi ◽

Mohammad Bohloul

Keyword(s):

Multipartite Entanglement ◽

Entanglement Measures

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Compatibility conditions from multipartite entanglement measures

Physical Review A ◽

10.1103/physreva.75.052324 ◽

2007 ◽

Vol 75 (5) ◽

Cited By ~ 11

Author(s):

Jian-Ming Cai ◽

Zheng-Wei Zhou ◽

Shun Zhang ◽

Guang-Can Guo

Keyword(s):

Multipartite Entanglement ◽

Compatibility Conditions ◽

Entanglement Measures

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WITNESSED ENTANGLEMENT

International Journal of Quantum Information ◽

10.1142/s0219749906001803 ◽

2006 ◽

Vol 04 (02) ◽

pp. 331-340 ◽

Cited By ~ 28

Author(s):

FERNANDO G. S. L. BRANDÃO ◽

REINALDO O. VIANNA

Keyword(s):

Multipartite Entanglement ◽

Mixed States ◽

Entanglement Measures ◽

Different Types

We present a new measure of entanglement for mixed states. It can be approximately computable for every state and can be used to quantify all different types of multipartite entanglement. We show that it satisfies the usual properties of a good entanglement quantifier and derive relations between it and other entanglement measures.

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Rescaling multipartite entanglement measures for mixed states

Applied Physics B ◽

10.1007/s00340-011-4864-x ◽

2012 ◽

Vol 106 (3) ◽

pp. 533-541 ◽

Cited By ~ 20

Author(s):

O. Viehmann ◽

C. Eltschka ◽

J. Siewert

Keyword(s):

Multipartite Entanglement ◽

Mixed States ◽

Entanglement Measures

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The role of localizable concurrence in quantum teleportation protocols

International Journal of Quantum Information ◽

10.1142/s0219749921500246 ◽

2021 ◽

Vol 19 (05) ◽

Author(s):

Mirko Consiglio ◽

Louis Zammit Mangion ◽

Tony John George Apollaro

Keyword(s):

Quantum Teleportation ◽

Quantum Information Processing ◽

Bell State ◽

Multipartite Entanglement ◽

Bell Measurement ◽

Classical Counterpart ◽

Entanglement Measures ◽

Classical Protocol ◽

Better Than

Teleporting an unknown qubit state is a paradigmatic quantum information processing task revealing the advantage of quantum communication protocols over their classical counterpart. For a teleportation protocol using a Bell state as quantum channel, the resource has been identified to be the concurrence. However, for mixed multipartite states the lack of computable entanglement measures has made the identification of the quantum resource responsible for this advantage more challenging. Here, by building on previous results showing that localizable concurrence is the necessary resource for controlled quantum teleportation, we show that any teleportation protocol using an arbitrary multipartite state, that includes a Bell measurement, requires a nonvanishing localizable concurrence between two of its parties to perform better than the classical protocol. By first analyzing Greenberger–Horne–Zeilinger (GHZ) channel and GHZ measurement teleportation protocol, in the presence of GHZ-symmetric-preserving noise, we compare different multipartite entanglement measures with the fidelity of teleportation, and we find that the protocol performs better than the classical protocol when all multipartite entanglement measures vanish, except for the localizable concurrence. Finally, we extend our proof to an arbitrary teleportation protocol with an arbitrary multipartite entangled channel.

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