Monotone Riemannian Metrics and Negativity of Entanglement

Prasenjit Deb

Published 2015-05-18Version 1

Monotone Riemannian metrics are very useful for information-theoretic and statistical considerations on the quantum state space. In this article, considering the quantum state space being spanned by 2x2 density matrices, we determine a particular Riemannian metric for a state $\rho$ . Then we show that if $\rho$ gets entangled with another quantum state, the negativity of the generated entangled state is, upto a constant factor, equals to square root of that particular Riemannian metric. Our result clearly relates a geometric quantity to a measure of entanglement. Moreover, the result establishes the possibility of understanding quantum correlations through geometric approach.