Essentially entangled component of multipartite mixed quantum states, its properties, and an efficient algorithm for its extraction

V. M. Akulin, G. A. Kabatiansky, A. Mandilara

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Abstract

Using geometric means, we first consider a density matrix decomposition of a multipartite quantum system of a finite dimension into two density matrices: a separable one, also known as the best separable approximation, and an essentially entangled one, which contains no product state components. We show that this convex decomposition can be achieved in practice with the help of a linear programming algorithm that scales in the general case polynomially with the system dimension. We illustrate the algorithm implementation with an example of a composite system of dimension 12 that undergoes a loss of coherence due to classical noise and we trace the time evolution of its essentially entangled component. We suggest a "geometric" description of entanglement dynamics and demonstrate how it explains the well-known phenomena of sudden death and revival of multipartite entanglements. For a statistical weight loss of the essentially entangled component with time, its average entanglement content is not affected by the coherence loss.

Original languageEnglish
Article number042322
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume92
Issue number4
DOIs
Publication statusPublished - Oct 20 2015

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decomposition
linear programming
death
composite materials
products
approximation

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

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AB - Using geometric means, we first consider a density matrix decomposition of a multipartite quantum system of a finite dimension into two density matrices: a separable one, also known as the best separable approximation, and an essentially entangled one, which contains no product state components. We show that this convex decomposition can be achieved in practice with the help of a linear programming algorithm that scales in the general case polynomially with the system dimension. We illustrate the algorithm implementation with an example of a composite system of dimension 12 that undergoes a loss of coherence due to classical noise and we trace the time evolution of its essentially entangled component. We suggest a "geometric" description of entanglement dynamics and demonstrate how it explains the well-known phenomena of sudden death and revival of multipartite entanglements. For a statistical weight loss of the essentially entangled component with time, its average entanglement content is not affected by the coherence loss.

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