Geometry of quantum state space and entanglement

TL;DR

This paper explores the geometric structure of quantum state space, establishing explicit relationships between measures of entanglement and Riemannian metrics for various bipartite states, extending previous findings.

Contribution

It generalizes the connection between entanglement measures and geometric metrics to a broader class of bipartite quantum states.

Findings

Negativity relates to Riemannian metric for entangled states

Explicit formulas linking entanglement measures and geometry

Extension of geometric-entanglement relations beyond qubits

Abstract

Recently, an explicit relation between a measure of entanglement and a geometric entity has been reported in Quantum Inf. Process. (2016) 15:1629-1638. It has been shown that if a qubit gets entangled with another ancillary qubit then negativity, up to a constant factor, is equal to square root of a specific Riemannian metric defined on the metric space corresponding to the state space of the qubit. In this article, we consider the different class of bi-partite entangled states and show explicit relation between two measures of entanglement and Riemannian metric.