Entanglement in bipartite X-states: Analytical results for the volume of states with positive partial transpose

Abstract

We provide an analytical formula for the volume ratio between bipartite X-states with positive partial transpose and all bipartite X-states. The result applies to arbitrary $m\times n$-bipartite systems and the volume expressions are derived with respect to the Hilbert-Schmidt measure.

13 pages

References in corpus (4)

• Monte Carlo sampling from the quantum state space. I
• Dyson Indices and Hilbert-Schmidt Separability Functions and Probabilities
• Volumes of conditioned bipartite state spaces
• Quantitative characterization of several entanglement detection criteria