On the partial transpose of fermionic Gaussian states. (27th May 2015)

• Record Type: Journal Article
• Authors: Eisler, Viktor; Zimborás, Zoltán
• Is Part Of: New journal of physics. Volume 17:Number 5(2015:May)
• Publication Date: 2015-05-27
• Subjects: quantum mechanics -- Gaussian states -- entanglement -- fermion systems -- negativity; Physics -- Periodicals; Physics; Periodicals; 530.05
• DOI: 10.1088/1367-2630/17/5/053048
• Languages: English
• ISSNs: 1367-2630

Abstract

Abstract: We consider Gaussian states of fermionic systems and study the action of the partial transposition on the density matrix. It is shown that, with a suitable choice of basis, these states are transformed into a linear combination of two Gaussian operators that are uniquely defined in terms of the covariance matrix of the original state. In case of a reflection symmetric geometry, this result can be used to efficiently calculate a lower bound for a well-known entanglement measure, the logarithmic negativity. Furthermore, exact expressions can be derived for traces involving integer powers of the partial transpose. The method can also be applied to the quantum Ising chain and the results show perfect agreement with the predictions of conformal field theory.