Lower bounds on the entanglement of formation for general Gaussian states

This article reviews and extends recent results concerning entanglement and frustration in multipartite systems which have some symmetry with respect to the ordering of the particles. Starting point of the discussion are Bell inequalities: their relation to frustration in classical systems and their satisfaction for quantum states which have a symmetric extension. We then discussed how more general global symmetries of multipartite systems constrain the entanglement between two neighboring particles. We prove that maximal entanglement (measured in terms of the entanglement of formation) is always attained for the ground state of a certain nearest neighbor interaction Hamiltonian having the considered symmetry with the achievable amount of entanglement being a function of the ground state energy. Systems of Gaussian states, i.e. quantum harmonic oscillators, are investigated in more detail and the results are compared to what is known about ordered qubit systems.

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Entanglement of Formation for Symmetric Gaussian States

Physical Review Letters ◽

10.1103/physrevlett.91.107901 ◽

2003 ◽

Vol 91 (10) ◽

Cited By ~ 218

Author(s):

G. Giedke ◽

M. M. Wolf ◽

O. Krüger ◽

R. F. Werner ◽

J. I. Cirac

Keyword(s):

Gaussian States ◽

Entanglement Of Formation

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Tight bounds for the entanglement of formation of Gaussian states

Physical Review A ◽

10.1103/physreva.89.012336 ◽

2014 ◽

Vol 89 (1) ◽

Cited By ~ 10

Author(s):

Fernando Nicacio ◽

Marcos C. de Oliveira

Keyword(s):

Gaussian States ◽

Entanglement Of Formation

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ENTANGLEMENT BOUNDS FOR A FAMILY OF TWO-MODE GAUSSIAN STATES

International Journal of Quantum Information ◽

10.1142/s0219749904000201 ◽

2004 ◽

Vol 02 (02) ◽

pp. 273-283 ◽

Cited By ~ 7

Author(s):

LI-ZHEN JIANG

Keyword(s):

Relative Entropy ◽

Upper Bound ◽

Gaussian States ◽

Entanglement Of Formation ◽

Coherent Information ◽

Relative Entropy Of Entanglement ◽

Quantum Gaussian States

I study a family of bipartite quantum Gaussian states with three parameters, calculate Gaussian entanglement of formation analytically and the upper bound of relative entropy of entanglement, compare them with the coherent information of the states. Based on the numerical observation, I determine the relative entropy of entanglement and distillable entanglement of the states with infinitive squeezing.

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