### 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 language | English |
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Article number | 042322 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 92 |

Issue number | 4 |

DOIs | |

Publication status | Published - Oct 20 2015 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*92*(4), [042322]. https://doi.org/10.1103/PhysRevA.92.042322

**Essentially entangled component of multipartite mixed quantum states, its properties, and an efficient algorithm for its extraction.** / Akulin, V. M.; Kabatiansky, G. A.; Mandilara, A.

Research output: Contribution to journal › Article

*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 92, no. 4, 042322. https://doi.org/10.1103/PhysRevA.92.042322

}

TY - JOUR

T1 - Essentially entangled component of multipartite mixed quantum states, its properties, and an efficient algorithm for its extraction

AU - Akulin, V. M.

AU - Kabatiansky, G. A.

AU - Mandilara, A.

PY - 2015/10/20

Y1 - 2015/10/20

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84946199305&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84946199305&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.92.042322

DO - 10.1103/PhysRevA.92.042322

M3 - Article

AN - SCOPUS:84946199305

VL - 92

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 4

M1 - 042322

ER -