Gaussian relative entropy of entanglement
Abstract
We calculate the relative entropy between two quantum Gaussian states with given correlation matrices by demonstrating a practical method of transforming one of the correlation matrices into an exponential quadratic operator matrix. We show that the closest Gaussian separable state achieving the Gaussian relative entropy of entanglement is at the border between separable and inseparable Gaussian state sets. For a twomode Gaussian state, the calculation of the Gaussian relative entropy of entanglement is greatly simplified by deducing a matrix with ten undetermined parameters to one with only three. The twomode Gaussian states are classified into four types. Numerical calculations strongly suggest that the Gaussian relative entropy of entanglement for each type is realized by a Gaussian separable state within the same type. For a symmetric Gaussian state it is strictly proven that the Gaussian relative entropy of entanglement is achieved by a symmetric Gaussian separable state.
 Publication:

Physical Review A
 Pub Date:
 June 2005
 DOI:
 10.1103/PhysRevA.71.062320
 arXiv:
 arXiv:quantph/0402109
 Bibcode:
 2005PhRvA..71f2320C
 Keywords:

 03.67.Mn;
 03.65.Ud;
 Entanglement production characterization and manipulation;
 Entanglement and quantum nonlocality;
 Quantum Physics
 EPrint:
 12 pages, 3 figures